Members Event

Event participants

Scott Walker, Governor, Wisconsin, United States
Chair: Justin Webb, Presenter, Today Programme, BBC Radio 4 

Jesper V. Olsen
Dec 1, 2005; 4:2010-2021
Technology

Invitation Only Research Event

Event participants

Daniel Finkelstein OBE, Associate Editor, The Times; Conservative Member of the House of Lords; Chairman, Onward 
Chair: Thomas Raines, Head, Europe Programme, Chatham House

15 October 2019

Webinar Research Event

Event participants

Ignacio Garcia Bercero, Director, Directorate General for Trade of the European Commission; European Union Visiting Fellow, Oxford University
Jennifer Hillman, Senior Fellow for Trade and International Political Economy, Council on Foreign Relations; Member, WTO Appellate Body, 2007 - 11
Chair: Marianne Schneider-Petsinger, Senior Research Fellow, US and Americas Programme, Chatham House

In my previous article on writing groups (which you can read here),  I talked about some popular ways writers connect. From online forums like the Mythic Scribes writing forums to community workshops, there’s no shortage of ways writers find each other, and just as many reasons they’re out there searching in the first place. In this follow-up article I’d like to explore some ways to start a writing group, and to keep a good group running by avoiding common pitfalls that lead to trouble.

What’s the Point?

Whether you’ve been searching for an established group and have had zero luck finding the right one, or you’re trying to start a specific group to fill a niche, the first thing to consider when starting a group is the scope—what you’re hoping to get from it. Writing solo can work for years, until one day…it just doesn’t, and it helps to know what you’re looking for in a writers’ group. Motivation, accountability, advice, feedback, critique, support—you name it, there’s a group for it, or at least other folks looking for the same thing.

Are you searching for a relaxed place for people to share their journey as writers?

Continue reading Writing Groups Part 2 at Mythic Scribes.

This article is part 3 of a series on Fantasy Fortifications by Toni Šušnjar.

The design of a fortification depends on its purpose and on the threats it is expected to face. A fortification facing only infantry-held weapons, one facing mechanical artillery, and one facing gunpowder artillery will all significantly differ in design characteristics. Some characteristics however will be the same – geography will always provide advantage (or disadvantage) in defending a fort or a city, and thus location has to be carefully chosen. In some cases, location may be good enough to allow the defender to skimp on certain design features – as seen with e.g. Klis fortress, where northern wall is waist-tall at best, thanks to its position on an inaccessible cliff (clissa). In other cases, disadvantageous terrain may have to be compensated with by massive man-made features.

General Design

In order to cope with development of artillery, design of fortifications changed with time. First fortifications, which only had to deal with handheld weapons, were simple wooden palisades. These were later supplemented with earthen ramparts

As siege weapons developed, fortifications grew both in height and thickness.

Continue reading Fantasy Fortifications — Part 3: Design at Mythic Scribes.

This article is part 4 of a series on Fantasy Fortifications by Toni Šušnjar.

Building a Fort

Build time of a castle, depending on design and available funds, may last from half a year to half a century. It also depends on the situation before the building: a ruined castle is a half-built castle after all, and rennovating (and/or updating) walls is much cheaper than building new ones. This can be seen with city of Dubrovnik, where (massive) medieval fortifications were, after the fall of Constantinople in 1453., reinforced with outer line of walls to reinforce them against cannon fire.

Both build time and extent of fortifications depend on material (financial, logistical, humane) capacities of the builder, as well as the perceived need. Many castles were never finished for lack of resources.

Builders are professionals; peasants, soldiers and other amateurs were used for muscle work only. This means that they have to be paid, and many in fact travel from a building place to a building place. Beaumaris Castle in England required 400 masons and 1,000 assistants to be built in a nearly record time (from 1278 to 1280).

Types of Castles
Motte and bailey castle

Motte and bailey castle is the earliest and simplest type of a castle.

Continue reading Fantasy Fortifications — Part 4: Types of Castles at Mythic Scribes.

19 December 2019

Webinar Research Event

Event participants

Ignacio Garcia Bercero, Director, Directorate General for Trade of the European Commission; European Union Visiting Fellow, Oxford University
Jennifer Hillman, Senior Fellow for Trade and International Political Economy, Council on Foreign Relations; Member, WTO Appellate Body, 2007 - 11
Chair: Marianne Schneider-Petsinger, Senior Research Fellow, US and Americas Programme, Chatham House

Cellular membranes are not homogenous mixtures of proteins; rather, they are segregated into microdomains on the basis of preferential association between specific lipids and proteins. These microdomains, called lipid rafts, are well known for their role in receptor signaling on the plasma membrane (PM) and are essential to such cellular functions as signal transduction and spatial organization of the PM. A number of disease states, including atherosclerosis and other cardiovascular disorders, may be caused by dysfunctional maintenance of lipid rafts. Lipid rafts do not occur only in the PM but also have been found in intracellular membranes and extracellular vesicles (EVs). Here, we focus on discussing newly discovered functions of lipid rafts and microdomains in intracellular membranes, including lipid and protein trafficking from the ER, Golgi bodies, and endosomes to the PM, and we examine lipid raft involvement in the production and composition of EVs. Because lipid rafts are small and transient, visualization remains challenging. Future work with advanced techniques will continue to expand our knowledge about the roles of lipid rafts in cellular functioning.

Expert

Expert

Invitation Only Research Event

Event participants

Dr Robin Niblett CMG, Director, Chatham House  
Toshiro Mutoh, Honorary Chairman, Daiwa Institute of Research; CEO, Tokyo Organising Committee of the Olympic and Paralympic Game
José Manuel Barroso, Senior Adviser, Chatham House; President of the European Commission (2004-14); Prime Minister of Portugal (2002-04)
Akihiko Tanaka, President, National Graduate Institute for Policy Studies

Sea ice is one of the least understood components of our climate. Naturally its abundance or scarcity is a telling sign of climate change, but sea ice is also an important actor in change as well, insulating the ocean and reflecting sunlight. A branch of mathematics called percolation theory helps explain how salt water travels through sea ice, a process that is crucial both to the amount of sea ice present and to the microscopic communities that sustain polar ecosystems. By taking samples, doing on-site experiments, and then incorporating the data into models of porous materials, mathematicians are working to understand sea ice and help refine climate predictions. Using probability, numerical analysis, and partial differential equations, researchers have recently shown that the permeability of sea ice is similar to that of some sedimentary rocks in the earth.s crust, even though the substances are otherwise dissimilar. One major difference between the two is the drastic changes in permeability of sea ice, from total blockage to clear passage, that occur over a range of just a few degrees. This difference can have a major effect on measurements by satellite, which provide information on the extent and thickness of sea ice. Results about sea ice will not only make satellite measurements more reliable, but they can also be applied to descriptions of lung and bone porosity, and to understanding ice on other planets. Image: Pancake ice in Antarctica, courtesy of Ken Golden. For More Information: "Thermal evolution of permeability and microstructure in sea ice," K. M. Golden, et al., Geophysical Research Letters, August 28, 2007.

Sea ice is one of the least understood components of our climate. Naturally its abundance or scarcity is a telling sign of climate change, but sea ice is also an important actor in change as well, insulating the ocean and reflecting sunlight. A branch of mathematics called percolation theory helps explain how salt water travels through sea ice, a process that is crucial both to the amount of sea ice present and to the microscopic communities that sustain polar ecosystems. By taking samples, doing on-site experiments, and then incorporating the data into models of porous materials, mathematicians are working to understand sea ice and help refine climate predictions. Using probability, numerical analysis, and partial differential equations, researchers have recently shown that the permeability of sea ice is similar to that of some sedimentary rocks in the earth.s crust, even though the substances are otherwise dissimilar. One major difference between the two is the drastic changes in permeability of sea ice, from total blockage to clear passage, that occur over a range of just a few degrees. This difference can have a major effect on measurements by satellite, which provide information on the extent and thickness of sea ice. Results about sea ice will not only make satellite measurements more reliable, but they can also be applied to descriptions of lung and bone porosity, and to understanding ice on other planets. Image: Pancake ice in Antarctica, courtesy of Ken Golden. For More Information: "Thermal evolution of permeability and microstructure in sea ice," K. M. Golden, et al., Geophysical Research Letters, August 28, 2007.

Sea ice is one of the least understood components of our climate. Naturally its abundance or scarcity is a telling sign of climate change, but sea ice is also an important actor in change as well, insulating the ocean and reflecting sunlight. A branch of mathematics called percolation theory helps explain how salt water travels through sea ice, a process that is crucial both to the amount of sea ice present and to the microscopic communities that sustain polar ecosystems. By taking samples, doing on-site experiments, and then incorporating the data into models of porous materials, mathematicians are working to understand sea ice and help refine climate predictions. Using probability, numerical analysis, and partial differential equations, researchers have recently shown that the permeability of sea ice is similar to that of some sedimentary rocks in the earth.s crust, even though the substances are otherwise dissimilar. One major difference between the two is the drastic changes in permeability of sea ice, from total blockage to clear passage, that occur over a range of just a few degrees. This difference can have a major effect on measurements by satellite, which provide information on the extent and thickness of sea ice. Results about sea ice will not only make satellite measurements more reliable, but they can also be applied to descriptions of lung and bone porosity, and to understanding ice on other planets. Image: Pancake ice in Antarctica, courtesy of Ken Golden. For More Information: "Thermal evolution of permeability and microstructure in sea ice," K. M. Golden, et al., Geophysical Research Letters, August 28, 2007.

Sea ice is one of the least understood components of our climate. Naturally its abundance or scarcity is a telling sign of climate change, but sea ice is also an important actor in change as well, insulating the ocean and reflecting sunlight. A branch of mathematics called percolation theory helps explain how salt water travels through sea ice, a process that is crucial both to the amount of sea ice present and to the microscopic communities that sustain polar ecosystems. By taking samples, doing on-site experiments, and then incorporating the data into models of porous materials, mathematicians are working to understand sea ice and help refine climate predictions. Using probability, numerical analysis, and partial differential equations, researchers have recently shown that the permeability of sea ice is similar to that of some sedimentary rocks in the earth.s crust, even though the substances are otherwise dissimilar. One major difference between the two is the drastic changes in permeability of sea ice, from total blockage to clear passage, that occur over a range of just a few degrees. This difference can have a major effect on measurements by satellite, which provide information on the extent and thickness of sea ice. Results about sea ice will not only make satellite measurements more reliable, but they can also be applied to descriptions of lung and bone porosity, and to understanding ice on other planets. Image: Pancake ice in Antarctica, courtesy of Ken Golden. For More Information: "Thermal evolution of permeability and microstructure in sea ice," K. M. Golden, et al., Geophysical Research Letters, August 28, 2007.

Stents are expandable tubes that are inserted into blocked or damaged blood vessels. They offer a practical way to treat coronary artery disease, repairing vessels and keeping them open so that blood can flow freely. When stents work, they are a great alternative to radical surgery, but they can deteriorate or become dislodged. Mathematical models of blood vessels and stents are helping to determine better shapes and materials for the tubes. These models are so accurate that the FDA is considering requiring mathematical modeling in the design of stents before any further testing is done, to reduce the need for expensive experimentation. Precise modeling of the entire human vascular system is far beyond the reach of current computational power, so researchers focus their detailed models on small subsections, which are coupled with simpler models of the rest of the system. The Navier-Stokes equations are used to represent the flow of blood and its interaction with vessel walls. A mathematical proof was the central part of recent research that led to the abandonment of one type of stent and the design of better ones. The goal now is to create better computational fluid-vessel models and stent models to improve the treatment and prediction of coronary artery disease the major cause of heart attacks. For More Information: Design of Optimal Endoprostheses Using Mathematical Modeling, Canic, Krajcer, and Lapin, Endovascular Today, May 2006.

Stents are expandable tubes that are inserted into blocked or damaged blood vessels. They offer a practical way to treat coronary artery disease, repairing vessels and keeping them open so that blood can flow freely. When stents work, they are a great alternative to radical surgery, but they can deteriorate or become dislodged. Mathematical models of blood vessels and stents are helping to determine better shapes and materials for the tubes. These models are so accurate that the FDA is considering requiring mathematical modeling in the design of stents before any further testing is done, to reduce the need for expensive experimentation. Precise modeling of the entire human vascular system is far beyond the reach of current computational power, so researchers focus their detailed models on small subsections, which are coupled with simpler models of the rest of the system. The Navier-Stokes equations are used to represent the flow of blood and its interaction with vessel walls. A mathematical proof was the central part of recent research that led to the abandonment of one type of stent and the design of better ones. The goal now is to create better computational fluid-vessel models and stent models to improve the treatment and prediction of coronary artery disease the major cause of heart attacks. For More Information: Design of Optimal Endoprostheses Using Mathematical Modeling, Canic, Krajcer, and Lapin, Endovascular Today, May 2006.

Archimedes was one of the most brilliant people ever, on a par with Einstein and Newton. Yet very little of what he wrote still exists because of the passage of time, and because many copies of his works were erased and the cleaned pages were used again. One of those written-over works (called a palimpsest) has resurfaced, and advanced digital imaging techniques using statistics and linear algebra have revealed his previously unknown discoveries in combinatorics and calculus. This leads to a question that would stump even Archimedes: How much further would mathematics and science have progressed had these discoveries not been erased? One of the most dramatic revelations of Archimedes. work was done using X-ray fluorescence. A painting, forged in the 1940s by one of the book.s former owners, obscured the original text, but X-rays penetrated the painting and highlighted the iron in the ancient ink, revealing a page of Archimedes. treatise The Method of Mechanical Theorems. The entire process of uncovering this and his other ideas is made possible by modern mathematics and physics, which are built on his discoveries and techniques. This completion of a circle of progress is entirely appropriate since one of Archimedes. accomplishments that wasn.t lost is his approximation of pi. For More Information: The Archimedes Codex, Reviel Netz and William Noel, 2007.

Archimedes was one of the most brilliant people ever, on a par with Einstein and Newton. Yet very little of what he wrote still exists because of the passage of time, and because many copies of his works were erased and the cleaned pages were used again. One of those written-over works (called a palimpsest) has resurfaced, and advanced digital imaging techniques using statistics and linear algebra have revealed his previously unknown discoveries in combinatorics and calculus. This leads to a question that would stump even Archimedes: How much further would mathematics and science have progressed had these discoveries not been erased? One of the most dramatic revelations of Archimedes. work was done using X-ray fluorescence. A painting, forged in the 1940s by one of the book.s former owners, obscured the original text, but X-rays penetrated the painting and highlighted the iron in the ancient ink, revealing a page of Archimedes. treatise The Method of Mechanical Theorems. The entire process of uncovering this and his other ideas is made possible by modern mathematics and physics, which are built on his discoveries and techniques. This completion of a circle of progress is entirely appropriate since one of Archimedes. accomplishments that wasn.t lost is his approximation of pi. For More Information: The Archimedes Codex, Reviel Netz and William Noel, 2007.

What.s in store for our climate and us? It.s an extraordinarily complex question whose answer requires physics, chemistry, earth science, and mathematics (among other subjects) along with massive computing power. Mathematicians use partial differential equations to model the movement of the atmosphere; dynamical systems to describe the feedback between land, ocean, air, and ice; and statistics to quantify the uncertainty of current projections. Although there is some discrepancy among different climate forecasts, researchers all agree on the tremendous need for people to join this effort and create new approaches to help understand our climate. It.s impossible to predict the weather even two weeks in advance, because almost identical sets of temperature, pressure, etc. can in just a few days result in drastically different weather. So how can anyone make a prediction about long-term climate? The answer is that climate is an average of weather conditions. In the same way that good predictions about the average height of 100 people can be made without knowing the height of any one person, forecasts of climate years into the future are feasible without being able to predict the conditions on a particular day. The challenge now is to gather more data and use subjects such as fluid dynamics and numerical methods to extend today.s 20-year projections forward to the next 100 years. For More Information: Mathematics of Climate Change: A New Discipline for an Uncertain Century, Dana Mackenzie, 2007.

What.s in store for our climate and us? It.s an extraordinarily complex question whose answer requires physics, chemistry, earth science, and mathematics (among other subjects) along with massive computing power. Mathematicians use partial differential equations to model the movement of the atmosphere; dynamical systems to describe the feedback between land, ocean, air, and ice; and statistics to quantify the uncertainty of current projections. Although there is some discrepancy among different climate forecasts, researchers all agree on the tremendous need for people to join this effort and create new approaches to help understand our climate. It.s impossible to predict the weather even two weeks in advance, because almost identical sets of temperature, pressure, etc. can in just a few days result in drastically different weather. So how can anyone make a prediction about long-term climate? The answer is that climate is an average of weather conditions. In the same way that good predictions about the average height of 100 people can be made without knowing the height of any one person, forecasts of climate years into the future are feasible without being able to predict the conditions on a particular day. The challenge now is to gather more data and use subjects such as fluid dynamics and numerical methods to extend today.s 20-year projections forward to the next 100 years. For More Information: Mathematics of Climate Change: A New Discipline for an Uncertain Century, Dana Mackenzie, 2007.

One of the most useful tools in analyzing the spread of disease is a system of evolutionary equations that reflects the dynamics among three distinct categories of a population: those susceptible (S) to a disease, those infected (I) with it, and those recovered (R) from it. This SIR model is applicable to a range of diseases, from smallpox to the flu. To predict the impact of a particular disease it is crucial to determine certain parameters associated with it, such as the average number of people that a typical infected person will infect. Researchers estimate these parameters by applying statistical methods to gathered data, which aren.t complete because, for example, some cases aren.t reported. Armed with reliable models, mathematicians help public health officials battle the complex, rapidly changing world of modern disease. Today.s models are more sophisticated than those of even a few years ago. They incorporate information such as contact periods that vary with age (young people have contact with one another for a longer period of time than do adults from different households), instead of assuming equal contact periods for everyone. The capacity to treat variability makes it possible to predict the effectiveness of targeted vaccination strategies to combat the flu, for instance. Some models now use graph theory and matrices to represent networks of social interactions, which are important in understanding how far and how fast a given disease will spread. For More Information: Mathematical Models in Population Biology and Epidemiology, Fred Brauer and Carlos Castillo-Chavez.

One of the most useful tools in analyzing the spread of disease is a system of evolutionary equations that reflects the dynamics among three distinct categories of a population: those susceptible (S) to a disease, those infected (I) with it, and those recovered (R) from it. This SIR model is applicable to a range of diseases, from smallpox to the flu. To predict the impact of a particular disease it is crucial to determine certain parameters associated with it, such as the average number of people that a typical infected person will infect. Researchers estimate these parameters by applying statistical methods to gathered data, which aren.t complete because, for example, some cases aren.t reported. Armed with reliable models, mathematicians help public health officials battle the complex, rapidly changing world of modern disease. Today.s models are more sophisticated than those of even a few years ago. They incorporate information such as contact periods that vary with age (young people have contact with one another for a longer period of time than do adults from different households), instead of assuming equal contact periods for everyone. The capacity to treat variability makes it possible to predict the effectiveness of targeted vaccination strategies to combat the flu, for instance. Some models now use graph theory and matrices to represent networks of social interactions, which are important in understanding how far and how fast a given disease will spread. For More Information: Mathematical Models in Population Biology and Epidemiology, Fred Brauer and Carlos Castillo-Chavez.

Mathematics has helped investigators in several major cases of human rights abuses and election fraud. Among them: The 2009 election in Iran. A mathematical result known as Benford's Law states that the leading digits of truly random numbers aren't distributed uniformly, as might be expected. Instead, smaller digits, such as 1's, appear much more frequently than larger digits, such as 9's. Benford's Law and other statistical tests have been applied to the 2009 election and suggest strongly that the final totals are suspicious. Ethnic cleansing. When Slobodan Milosevic went on trial, it was his contention that the mass exodus of ethnic Albanians from Kosovo was due to NATO bombings and the activities of the Albanian Kosovo Liberation Army rather than anything he had ordered. A team collected data on the flow of refugees to test those hypotheses and was able to refute Milosevic's claim in its entirety. Guatemalan disappearances. Here, statistics is being used to extract information from over 80 million National Police archive pages related to about 200,000 deaths and disappearances. Sampling techniques give investigators an accurate representation of the records without them having to read every page. Families are getting long-sought after proof of what happened to their relatives, and investigators are uncovering patterns and motives behind the abductions and murders. Tragically, the people have disappeared. But because of this analysis, the facts won't. For More Information: Killings and Refugee Flow in Kosovo, March-June 1999, Ball et al., 2002.

Mathematics has helped investigators in several major cases of human rights abuses and election fraud. Among them: The 2009 election in Iran. A mathematical result known as Benford's Law states that the leading digits of truly random numbers aren't distributed uniformly, as might be expected. Instead, smaller digits, such as 1's, appear much more frequently than larger digits, such as 9's. Benford's Law and other statistical tests have been applied to the 2009 election and suggest strongly that the final totals are suspicious. Ethnic cleansing. When Slobodan Milosevic went on trial, it was his contention that the mass exodus of ethnic Albanians from Kosovo was due to NATO bombings and the activities of the Albanian Kosovo Liberation Army rather than anything he had ordered. A team collected data on the flow of refugees to test those hypotheses and was able to refute Milosevic's claim in its entirety. Guatemalan disappearances. Here, statistics is being used to extract information from over 80 million National Police archive pages related to about 200,000 deaths and disappearances. Sampling techniques give investigators an accurate representation of the records without them having to read every page. Families are getting long-sought after proof of what happened to their relatives, and investigators are uncovering patterns and motives behind the abductions and murders. Tragically, the people have disappeared. But because of this analysis, the facts won't. For More Information: Killings and Refugee Flow in Kosovo, March-June 1999, Ball et al., 2002.

It doesn't take a perfect storm to generate a rogue wave-an open-ocean wave much steeper and more massive than its neighbors that appears with little or no warning. Sometimes winds and currents collide causing waves to combine nonlinearly and produce these towering walls of water. Mathematicians and other researchers are collecting data from rogue waves and modeling them with partial differential equations to understand how and why they form. A deeper understanding of both their origins and their frequency will result in safer shipping and offshore platform operations. Since rogue waves are rare and short lived (fortunately), studying them is not easy. So some researchers are experimenting with light to create rogue waves in a different medium. Results of these experiments are consistent with sailors' claims that rogues, like other unusual events, are more frequent than what is predicted by standard models. The standard models had assumed a bell-shaped distribution for wave heights, and anticipated a rogue wave about once every 10,000 years. This purported extreme unlikelihood led designers and builders to not account for their potential catastrophic effects. Today's recognition of rogues as rare, but realistic, possibilities could save the shipping industry billions of dollars and hundreds of lives. For More Information: "Dashing Rogues", Sid Perkins, Science News, November 18, 2006.

It doesn't take a perfect storm to generate a rogue wave-an open-ocean wave much steeper and more massive than its neighbors that appears with little or no warning. Sometimes winds and currents collide causing waves to combine nonlinearly and produce these towering walls of water. Mathematicians and other researchers are collecting data from rogue waves and modeling them with partial differential equations to understand how and why they form. A deeper understanding of both their origins and their frequency will result in safer shipping and offshore platform operations. Since rogue waves are rare and short lived (fortunately), studying them is not easy. So some researchers are experimenting with light to create rogue waves in a different medium. Results of these experiments are consistent with sailors' claims that rogues, like other unusual events, are more frequent than what is predicted by standard models. The standard models had assumed a bell-shaped distribution for wave heights, and anticipated a rogue wave about once every 10,000 years. This purported extreme unlikelihood led designers and builders to not account for their potential catastrophic effects. Today's recognition of rogues as rare, but realistic, possibilities could save the shipping industry billions of dollars and hundreds of lives. For More Information: "Dashing Rogues", Sid Perkins, Science News, November 18, 2006.

As difficult as it is to do the census, the ensuing process of determining the number of congressional seats for each state can be even harder. The basic premise, that the proportion of each state's delegation in the House should match its proportion of the U.S. population, is simple enough. The difficulty arises when deciding what to do with the fractions that inevitably arise (e.g., New York can't have 28.7 seats). Over the past 200 years, several methods of apportioning seats have been used. Many sound good but can lead to paradoxes, such as an increase in the total number of House seats actually resulting in a reduction of a state's delegation. The method used since the 1940s, whose leading proponent was a mathematician, is one that avoids such paradoxes. A natural question is Why 435 seats? Nothing in the Constitution mandates this number, although there is a prohibition against having more than one seat per 30,000 people. One model, based on the need for legislators to communicate with their constituents and with each other, uses algebra and calculus to show that the ideal assembly size is the cube root of the population it represents. Remarkably, the size of the House mirrored this rule until the early 1900s. To obey the rule now would require an increase to 670, which would presumably both better represent the population and increase the chances that the audience in the seats for those late speeches would outnumber the speaker. For More Information: "E pluribus confusion", Barry Cipra, American Scientist, July-August 2010.

As difficult as it is to do the census, the ensuing process of determining the number of congressional seats for each state can be even harder. The basic premise, that the proportion of each state's delegation in the House should match its proportion of the U.S. population, is simple enough. The difficulty arises when deciding what to do with the fractions that inevitably arise (e.g., New York can't have 28.7 seats). Over the past 200 years, several methods of apportioning seats have been used. Many sound good but can lead to paradoxes, such as an increase in the total number of House seats actually resulting in a reduction of a state's delegation. The method used since the 1940s, whose leading proponent was a mathematician, is one that avoids such paradoxes. A natural question is Why 435 seats? Nothing in the Constitution mandates this number, although there is a prohibition against having more than one seat per 30,000 people. One model, based on the need for legislators to communicate with their constituents and with each other, uses algebra and calculus to show that the ideal assembly size is the cube root of the population it represents. Remarkably, the size of the House mirrored this rule until the early 1900s. To obey the rule now would require an increase to 670, which would presumably both better represent the population and increase the chances that the audience in the seats for those late speeches would outnumber the speaker. For More Information: "E pluribus confusion", Barry Cipra, American Scientist, July-August 2010.

A triple cork is a spinning jump in which the snowboarder is parallel to the ground three times while in the air. Such a jump had never been performed in a competition before 2011, which prompted ESPN.s Sport Science program to ask math professor Tim Chartier if it could be done under certain conditions. Originally doubtful, he and a recent math major graduate used differential equations, vector analysis, and calculus to discover that yes, a triple cork was indeed possible. A few days later, boarder Torstein Horgmo landed a successful triple cork at the X-Games (which presumably are named for everyone.s favorite variable). Snowboarding is not the only sport in which modern athletes and coaches seek answers from mathematics. Swimming and bobsledding research involves computational fluid dynamics to analyze fluid flow so as to decrease drag. Soccer and basketball analysts employ graph and network theory to chart passes and quantify team performance. And coaches in the NFL apply statistics and game theory to focus on the expected value of a play instead of sticking with the traditional Square root of 9 yards and a cloud of dust.

A triple cork is a spinning jump in which the snowboarder is parallel to the ground three times while in the air. Such a jump had never been performed in a competition before 2011, which prompted ESPN.s Sport Science program to ask math professor Tim Chartier if it could be done under certain conditions. Originally doubtful, he and a recent math major graduate used differential equations, vector analysis, and calculus to discover that yes, a triple cork was indeed possible. A few days later, boarder Torstein Horgmo landed a successful triple cork at the X-Games (which presumably are named for everyone.s favorite variable). Snowboarding is not the only sport in which modern athletes and coaches seek answers from mathematics. Swimming and bobsledding research involves computational fluid dynamics to analyze fluid flow so as to decrease drag. Soccer and basketball analysts employ graph and network theory to chart passes and quantify team performance. And coaches in the NFL apply statistics and game theory to focus on the expected value of a play instead of sticking with the traditional Square root of 9 yards and a cloud of dust.

Nothing can prevent a tsunami from happening they are enormously powerful events of nature. But in many cases networks of seismic detectors, sea-level monitors and deep ocean buoys can allow authorities to provide adequate warning to those at risk. Mathematical models constructed from partial differential equations use the generated data to determine estimates of the speed and magnitude of a tsunami and its arrival time on coastlines. These models may predict whether a trough or a crest will be the first to arrive on shore. In only about half the cases (not all) does the trough arrive first, making the water level recede dramatically before the onslaught of the crest. Mathematics also helps in the placement of detectors and monitors. Researchers use geometry and population data to find the best locations for the sensors that will alert the maximum number of people. Once equipment is in place, warning centers collect and process data from many seismic stations to determine if an earthquake is the type that will generate a dangerous tsunami. All that work must wait until an event occurs because it is currently very hard to predict earthquakes. People on coasts far from an earthquake-generated tsunami may have hours to take action, but for those closer it.s a matter of minutes. The crest of a tsunami wave can travel at 450 miles per hour in open water, so fast algorithms for solving partial differential equations are essential. For More Information: Surface Water Waves and Tsunamis, Walter Craig, Journal of Dynamics and Differential Equations, Vol. 18, no. 3 (2006), pp. 525-549.

It.s often a challenge to get from Point A to Point B in normal circumstances, but after a disaster it can be almost impossible to transport food, water, and clothing from the usual supply points to the people in desperate need. A new mathematical model employs probability and nonlinear programming to design supply chains that have the best chance of functioning after a disaster. For each region or country, the model generates a robust chain of supply and delivery points that can respond to the combination of disruptions in the network and increased needs of the population. Math also helps medical agencies operate more efficiently during emergencies, such as an infectious outbreak. Fluid dynamics and combinatorial optimization are applied to facility layout and epidemiological models to allocate resources and improve operations while minimizing total infection within dispensing facilities. This helps ensure fast, effective administering of vaccines and other medicines. Furthermore, solution times are fast enough that officials can input up-to-the-minute data specific to their situation and make any necessary redistribution of supplies or staff in real time. For More Information: Supply Chain Network Economics: Dynamics of Prices, Flows, and Profits, Anna Nagurney, 2006.

The heart.s function of pumping blood may seem fairly simple but the underlying mechanisms and electrical impulses that maintain a healthy rhythm are extremely complex. Many areas of mathematics, including differential equations, dynamical systems, and topology help model the electrical behavior of cardiac cells, the connections between those cells and the heart.s overall geometry. Researchers aim to gain a better understanding of the normal operation of the heart, as well as learn how to diagnose the onset of abnormalities and correct them. Of the many things that can go wrong with a heart.s rhythm, some measure of unpredictability is (surprisingly) not one of them. A healthy heartbeat is actually quite chaotic not regular at all. Furthermore, beat patterns become less chaotic as people age and heart function diminishes. In fact, one researcher recommends that patients presented with a new medication should ask their doctors, "What is this drug going to do to my fractal dimensionality?" For More Information: Taking Mathematics to Heart: Mathematical Challenges in Cardiac Electrophysiology, John W. Cain, Notices of the AMS, April 2011, pp. 542-549.

Mathematics contributes in many ways to the process of converting wind power into usable energy. Large-scale weather models are used to find suitable locations for wind farms, while more narrowly focused models incorporating interactions arising from factors such as wake effects and turbulence specify how to situate individual turbines within a farm. In addition, computational fluid dynamics describes air flow and drag around turbines. This helps determine the optimal shapes for the blades, both structurally and aerodynamically, to extract as much energy as possible, and keep noise levels and costs down. Mathematics also helps answer two fundamental questions about wind turbines. First, why three blades? Turbines with fewer blades extract less energy and are noisier (because the blades must turn faster). Those with more than three blades would capture more energy but only about three percent more, which doesn.t justify the increased cost. Second, what percentage of wind energy can a turbine extract? Calculus and laws of conservation provide the justification for Betz Law, which states that no wind turbine can capture more than 60% of the energy in the wind. Modern turbines generally gather 40-50%. So the answer to someone who touts a turbine that can capture 65% of wind energy is "All Betz" are off. For More Information: Wind Energy Explained: Theory, Design and Application, Manwell, McGowan, and Rogers, 2010.

Some of the simplest and most well-known curves parabolas and ellipses, which can be traced back to ancient Greece are also among the most useful. Parabolas have a reflective property that is employed in many of today.s solar power technologies. Mirrors with a parabolic shape reflect all entering light to a single point called the focus, where the solar power is converted into usable energy. Ellipses, which have two foci, have a similar reflecting property that is exploited in a medical procedure called lithotripsy. Patients with kidney stones and gallstones are positioned in a tank shaped like half an ellipse so that the stones are at one focus. Acoustic waves sent from the other focus concentrate all their energy on the stones, pulverizing them without surgery. Math can sometimes throw you a curve, but that.s not necessarily a bad thing. Parabolas and ellipses are curves called conic sections. Another curve in this category is the hyperbola, which may have the most profound application of all the nature of the universe. In plane geometry, points that are a given distance from a fixed point form a circle. In space, points that are a given spacetime distance from a fixed point form one branch of a hyperbola. This is not an arbitrary mandate but instead a natural conclusion from the equations that result when the principle of relativity is reconciled with our notions of distance and causality. And although a great deal of time has elapsed since the discovery of conic sections, they continue to reap benefits today. For More Information: Practical Conic Sections: The Geometric Properties of Ellipses, Parabolas and Hyperbolas, J. W. Downs, 2010.

No one can predict who will commit a crime but in some cities math is helping detect areas where crimes have the greatest chance of occurring. Police then increase patrols in these "hot spots" in order to prevent crime. This innovative practice, called predictive policing, is based on large amounts of data collected from previous crimes, but it involves more than just maps and push pins. Predictive policing identifies hot spots by using algorithms similar to those used to predict aftershocks after major earthquakes. Just as aftershocks are more likely near a recent earthquake.s epicenter, so too are crimes, as criminals do indeed return to, or very close to, the scene of a crime. Cities employing this approach have seen crime rates drop and studies are underway to measure predictive policing.s part in that drop. One fact that has been determined concerns the nature of hot spots. Researchers using partial differential equations and bifurcation theory have discovered two types of hot spots, which respond quite differently to increased patrols. One type will shift to another area of the city while the other will disappear entirely. Unfortunately the two appear the same on the surface, so mathematicians and others are working to help police find ways to differentiate between the two so as to best allocate their resources.

There.s more mathematics involved in juggling than just trying to make sure that the number of balls (or chainsaws) that hits the ground stays at zero. Subjects such as combinatorics and abstract algebra help jugglers answer important questions, such as whether a particular juggling pattern can actually be juggled. For example, can balls be juggled so that the time period that each ball stays aloft alternates between five counts and one? The answer is Yes. Math also tells you that the number of balls needed for such a juggling pattern is the average of the counts, in this case three. Once a pattern is shown to be juggleable and the number of balls needed is known, equations of motion determine the speed with which each ball must be thrown and the maximum height it will attain. Obviously the harder a juggler throws, the faster and higher an object will go. Unfortunately hang time increases proportionally to the square root of the height, so the difficulty of keeping many objects in the air increases very quickly. Both math and juggling have been around for millennia yet questions still remain in both subjects. As two juggling mathematicians wrote, .A juggler, like a mathematician, is never finished: there is always another great unsolved problem.

There.s more mathematics involved in juggling than just trying to make sure that the number of balls (or chainsaws) that hits the ground stays at zero. Subjects such as combinatorics and abstract algebra help jugglers answer important questions, such as whether a particular juggling pattern can actually be juggled. For example, can balls be juggled so that the time period that each ball stays aloft alternates between five counts and one? The answer is Yes. Math also tells you that the number of balls needed for such a juggling pattern is the average of the counts, in this case three. Once a pattern is shown to be juggleable and the number of balls needed is known, equations of motion determine the speed with which each ball must be thrown and the maximum height it will attain. Obviously the harder a juggler throws, the faster and higher an object will go. Unfortunately hang time increases proportionally to the square root of the height, so the difficulty of keeping many objects in the air increases very quickly. Both math and juggling have been around for millennia yet questions still remain in both subjects. As two juggling mathematicians wrote, .A juggler, like a mathematician, is never finished: there is always another great unsolved problem.