May 16, 2013 ? The answer is yes, according to a paper in the SIAM Journal on Discrete Mathematics.
In a paper published in the journal last month, authors Anthony Bonato, Dieter Mitsche, and Pawel Pralat describe a mathematical model to disrupt flow of information in a complex real-world network, such as a terrorist organization, using minimal resources.
Terror networks are comparable in their structure to hierarchical organization in companies and certain online social networks, where information flows in one direction from a source, which produces the information or data, downwards to sinks, which consume it. Such networks are called hierarchical social networks.
"In such networks, the flow of information is often one way," explains author Pawel Pralat. "For example, a celebrity such as Justin Bieber sends out a tweet, which is sent to millions of his followers. These followers send out their own retweets, and so on. We may therefore view hierarchical social networks as directed networks without cycles, or directed acyclic graphs (DAGs)."
Here, there is no requirement for reciprocity (the celebrity does not necessarily follow his or her followers). Similarly, in a terrorist network, the leaders pass plans down to the foot soldiers, and usually only one messenger needs to receive the message for the plan to be executed.
Disruption of the flow of information would correspond to halting the spread of news in an online social network or intercepting messages in a terror network.
The authors propose a generalized stochastic model for the flow and disruption of information based on a two-player outdoor game called "Seepage," where players who depict agents attempt to block the movement of another player, an intruder, from a source node to a sink. "The game -- motivated by the 1973 eruption of the Eldfell volcano in Iceland -- displays some similarities to an approach used in mathematical counterterrorism, where special kinds of DAGs are used to model the disruption of terrorist cells," says Pralat.
The motivating eruption caused a major crisis at the time, as lava flow threatened to close off the harbor, the island's main source of income. In the game, inhabitants attempt to protect the harbor by pouring water on the volcanic lava to halt its progress. A mathematical model of the game pits two opponents against each other -- the sludge, or intruder, against the greens, or agents -- forming a directed acyclic graph, with one source (the top of the volcano) and many sinks representing the lake. The parameter, "seepage," represents the amount of contamination, and the "green number" corresponds to the number of agents required to halt it.
A previous study modeled terrorist cells as partially ordered sets (a special kind of DAG), which are often used in mathematics to analyze an ordering, sequencing, or arrangement of distinct objects. In such a system, terrorist plans are formulated by nodes at the top of the hierarchy, which represent the leaders or maximal nodes of the set. The plans are transmitted down to the nodes at the bottom: these represent foot soldiers in a terror network or minimal nodes in the set who would be presumed to carry out these plans. The assumption is that one messenger is sufficient for reception and execution of the plan. Thus, if the partially ordered set represents a courier network for a terrorist organization, the intention would be to block all routes from the maximal node to the minimal nodes by capturing or killing a subset of agents.
In this paper, the authors utilize the similarities in the previous terrorist cell model to Seepage, where greens try to prevent the sludge from moving to the sinks by blocking nodes. A number of different winning strategies employed by both players are explored when played on a DAG. The seepage and green number for disrupting a given hierarchical social network are analyzed.
The primary difference from the previous study's model is that the Seepage model is dynamic: greens can move and choose new sets of nodes over time. The authors determine that Seepage is a more realistic model of counterterrorism, as the agents do not necessarily act all at once, but over time.
The analysis is made in two types of terrorist network structures, as Pralat explains, "We consider two extreme profiles: one where the network is regular, where every agent has about the same number of connections. The second profile is power law, where some agents have many connections, but most have very few." This is analyzed by considering the total degree distribution of nodes in the DAG. In regular DAGs, each level of the DAG would have nodes with about the same out-degree (number of outgoing edges emanating from a node), while power law DAGs would have many more low-degree nodes and a few with high degrees.
Mathematical analysis allows the authors to determine what point in a network would be most effective for disrupting messages. "Our mathematical results reinforce the view that intercepting the information or message in a hierarchical social network following a power law is more difficult close to levels near the source. For regular networks, it does not matter as much where the message is disrupted," says Pralat. "Future work could look at more complex profiles of networks, along with developing effective algorithms for disrupting the flow of information in a DAG using our game-theoretic approach."
India's tigers are facing extinction owing to a collapse in the variety of their mating partners, say Cardiff University researchers.
They found that 93% of DNA variants found in tigers shot the period of the British Raj were not present in tigers today
Prof Mike Bruford said the genetic diversity needed for the species to survive had been "lost dramatically".
There are fewer than 2,000 tigers left worldwide, 60% in India.
The Cardiff university team collaborated with the National Centre for Biological Sciences in Bangalore, India on the research.
They had unprecedented access to the Natural History Museum of London's tiger collection which allowed them to identify the DNA variants in the tigers killed in the British Raj period from 1858 to 1947 but which have disappeared today.
Mechanised trophy hunting reduced the animal's numbers from 40,000 in a mere 100 years.
The territory occupied by the tiger has declined more than 50% during the last three generations and mating now only occurs in 7% of its historical territory.
Prof Bruford of the Cardiff School of Biosciences was one of the research's lead authors.
He said: "We found that genetic diversity has been lost dramatically compared to the Raj tigers and what diversity remains has become much more subdivided into the small (20-120 individual) populations that exist today.
"This is due to loss of habitat and habitat fragmentation, meaning lower population sizes, and the prevention of tigers from dispersing as they once would have, which means their gene pool is no longer mixing across the subcontinent.
Breeding programmes
"This is important because tigers, like all other species, need genetic diversity to survive - especially under climate change - so what diversity remains needs to be managed properly so that the Indian tiger does not become inbred, and retains its capacity to adapt."
Prof Bruford added: "Both conservationists and the Indian government must appreciate that the number of tigers alone is not enough to ensure the species' survival."
"They need to protect the whole spread of forest reserves because many reserves now have their own unique gene combinations, which might be useful for future breeding programmes.
"This study shows that genetic diversity can be lost and a new genetic structure can arise very quickly, if the effects of population collapse and habitat fragmentation are strong enough, so quick action is needed to stymie further demographic loss."
The report Demographic loss, genetic structure and the conservation implications for Indian tigersis published in the Proceedings of The Royal Society journal.
Funding for the project was provided by a Royal Society Collaborative Research Grant.
Same musicians: Brand new tunePublic release date: 14-May-2013 [ | E-mail | Share ]
Contact: Gina Kirchweger gxk@stowers.org 816-806-1036 Stowers Institute for Medical Research
KANSAS CITY, MOA small ensemble of musicians can produce an infinite number of melodies, harmonies and rhythms. So too, do a handful of workhorse signaling pathways that interact to construct multiple structures that comprise the vertebrate body. In fact, crosstalk between two of those pathwaysthose governed by proteins known as Notch and BMP (for Bone Morphogenetic Protein) receptorsoccurs over and over in processes as diverse as forming a tooth, sculpting a heart valve and building a brain.
A new study by Stowers Institute for Medical Research Investigator Ting Xie, Ph.D., reveals yet another duet played by Notch and BMP signals, this time with Notch calling the tune. That work, published in this week's online issue of PNAS, uses mouse genetics to demonstrate how one Notch family protein, Notch2, shapes an eye structure known as the ciliary body (CB), most likely by ensuring that BMP signals remain loud and clear.
In vertebrates, the CB encircles the lens and performs two tasks essential for normal vision. First, it contains a tiny muscle that reshapes the lens when you change focus, or "accommodate". And it also secretes liquid aqueous humor into the front compartment of the eye where it likely maintains correct eye pressure. Understanding CB construction is critical, as excessive pressure is one risk factor for glaucoma.
Eye development is a relatively new field for Xie, a recognized leader in the study of adult stem cells in the fruit fly: only recently did he branch out into mouse studies. "A few years ago I was asked to participate in a think tank-type meeting to discuss the potential application of cell therapy to treat glaucoma," he says. "I became interested in using retinal progenitor cells to treat diseases like glaucoma or macular degeneration. But I realized that first we needed to understand eye disease at the molecular level." The new study is an important step in that direction.
Previously, investigators knew that once cells that form the CB are established in an embryo, the BMP pathway drives their "morphogenesis", the term used by developmental biologists to describe the process of expanding and then sculpting a committed population of cells into a unique structure. "The Notch2 receptor was previously shown to be expressed in the developing mouse eye," explains Chris Tanzie, M.D., Ph.D., a former graduate student in the Xie lab and the study's co-first author. "But its function was unknown, and no one connected how various signaling pathways direct CB morphogenesis."
To determine what Notch2 was doing in the developing eye, the Stowers team constructed a conditional knockout mouse, meaning that the Notch2 gene is deleted from the genome only in eye cells that give rise to the CB. In normal newborn mice a series of cellular "folds" that characterize the CB emerges over the first 7 days of life. But the mutant knockout mice showed a complete absence of folds, dramatic evidence that Notch2 is required to elaborate a CB.
Furthermore, in normal mice a protein called Jagged-1, which activates Notch2, was expressed in cells adjacent to Notch2-expressing CB cells during the same developmental period. Strikingly, the team's collaborators in Richard Libby's laboratory at the University of Rochester Medical Center, were able to demonstrate that just like the Notch2 mutants, Jagged-1 conditional knockout mice showed almost total loss of CB fold structures, a major hint that Notch2 was switched on by Jagged1 to drive CB formation.
Biochemical and microarray analysis provided further explanation for defects observed after Notch2 loss. Comparison of normal and Notch2-mutant eye cells revealed that not only did cells of mutant mice lose BMP signaling but that expression of two proteins known to interfere with BMP increased in those cells.
"Up-regulation of BMP antagonists following Notch2 loss is an important observation," says Xie. "In other systems people often observe that Notch and BMP cooperatively regulate common targets by transcription factor collaboration at the transcriptional level, but this is a unique mechanism. We find that Notch2 keeps BMP signaling active by inhibiting its inhibitors."
The study's second co-first author is Yi Zhou, a University of Kansas Medical Center graduate student earning his Ph.D. in Xie's lab. "Our work reveals a novel link between Notch and BMP pathways potentially involved in the pathogenesis of glaucoma," says Zhou, noting one more tantalizing implication of the paper. "In addition, mutations in Jagged-1 and Notch2 are thought to underlie the human genetic disease known as Alagille Syndrome. Our work may lead to a better understanding of both."
Alagille Syndrome is an inherited childhood disorder causing defects in organ systems including liver, heart and the skeleton. Xie is equally intrigued by potential connections between his group's observations in the mouse eye and Alagille outcomes in humans. Nonetheless, he remains focused on nailing down how perturbation of the Jagged1-Notch2-BMP axis might cause eye disease.
"We now know how to build better mouse mutants to study CB development. In this work we show that Notch regulates BMP signaling but have not yet determined whether alterations in CB structure actually change interocular pressure," he says. "Answering that question is our future goal."
###
Other members of the Stowers team were Shuyi Chen, Ph.D., Michael Duncan, M.D., Karin Gaudenz, Ph.D., Christopher Seidel, Ph.D., Hua Li, Ph.D., Brandy Lewis, and Andrea Moran. Also contributing were Zhipeng Yan, Ph.D., Richard T. Libby, Ph.D., and Amy E. Kiernan, Ph.D, of the University of Rochester Medical Center.
The study was funded in part by the Stowers Institute for Medical Research, the March of Dimes, and a Research to Prevent Blindness Career Development Award.
About the Stowers Institute for Medical Research
The Stowers Institute for Medical Research is a non-profit, basic biomedical research organization dedicated to improving human health by studying the fundamental processes of life. Jim Stowers, founder of American Century Investments, and his wife, Virginia, opened the Institute in 2000. Since then, the Institute has spent over 900 million dollars in pursuit of its mission.
Currently, the Institute is home to nearly 550 researchers and support personnel; over 20 independent research programs; and more than a dozen technology-development and core facilities.
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AAAS and EurekAlert! are not responsible for the accuracy of news releases posted to EurekAlert! by contributing institutions or for the use of any information through the EurekAlert! system.
Same musicians: Brand new tunePublic release date: 14-May-2013 [ | E-mail | Share ]
Contact: Gina Kirchweger gxk@stowers.org 816-806-1036 Stowers Institute for Medical Research
KANSAS CITY, MOA small ensemble of musicians can produce an infinite number of melodies, harmonies and rhythms. So too, do a handful of workhorse signaling pathways that interact to construct multiple structures that comprise the vertebrate body. In fact, crosstalk between two of those pathwaysthose governed by proteins known as Notch and BMP (for Bone Morphogenetic Protein) receptorsoccurs over and over in processes as diverse as forming a tooth, sculpting a heart valve and building a brain.
A new study by Stowers Institute for Medical Research Investigator Ting Xie, Ph.D., reveals yet another duet played by Notch and BMP signals, this time with Notch calling the tune. That work, published in this week's online issue of PNAS, uses mouse genetics to demonstrate how one Notch family protein, Notch2, shapes an eye structure known as the ciliary body (CB), most likely by ensuring that BMP signals remain loud and clear.
In vertebrates, the CB encircles the lens and performs two tasks essential for normal vision. First, it contains a tiny muscle that reshapes the lens when you change focus, or "accommodate". And it also secretes liquid aqueous humor into the front compartment of the eye where it likely maintains correct eye pressure. Understanding CB construction is critical, as excessive pressure is one risk factor for glaucoma.
Eye development is a relatively new field for Xie, a recognized leader in the study of adult stem cells in the fruit fly: only recently did he branch out into mouse studies. "A few years ago I was asked to participate in a think tank-type meeting to discuss the potential application of cell therapy to treat glaucoma," he says. "I became interested in using retinal progenitor cells to treat diseases like glaucoma or macular degeneration. But I realized that first we needed to understand eye disease at the molecular level." The new study is an important step in that direction.
Previously, investigators knew that once cells that form the CB are established in an embryo, the BMP pathway drives their "morphogenesis", the term used by developmental biologists to describe the process of expanding and then sculpting a committed population of cells into a unique structure. "The Notch2 receptor was previously shown to be expressed in the developing mouse eye," explains Chris Tanzie, M.D., Ph.D., a former graduate student in the Xie lab and the study's co-first author. "But its function was unknown, and no one connected how various signaling pathways direct CB morphogenesis."
To determine what Notch2 was doing in the developing eye, the Stowers team constructed a conditional knockout mouse, meaning that the Notch2 gene is deleted from the genome only in eye cells that give rise to the CB. In normal newborn mice a series of cellular "folds" that characterize the CB emerges over the first 7 days of life. But the mutant knockout mice showed a complete absence of folds, dramatic evidence that Notch2 is required to elaborate a CB.
Furthermore, in normal mice a protein called Jagged-1, which activates Notch2, was expressed in cells adjacent to Notch2-expressing CB cells during the same developmental period. Strikingly, the team's collaborators in Richard Libby's laboratory at the University of Rochester Medical Center, were able to demonstrate that just like the Notch2 mutants, Jagged-1 conditional knockout mice showed almost total loss of CB fold structures, a major hint that Notch2 was switched on by Jagged1 to drive CB formation.
Biochemical and microarray analysis provided further explanation for defects observed after Notch2 loss. Comparison of normal and Notch2-mutant eye cells revealed that not only did cells of mutant mice lose BMP signaling but that expression of two proteins known to interfere with BMP increased in those cells.
"Up-regulation of BMP antagonists following Notch2 loss is an important observation," says Xie. "In other systems people often observe that Notch and BMP cooperatively regulate common targets by transcription factor collaboration at the transcriptional level, but this is a unique mechanism. We find that Notch2 keeps BMP signaling active by inhibiting its inhibitors."
The study's second co-first author is Yi Zhou, a University of Kansas Medical Center graduate student earning his Ph.D. in Xie's lab. "Our work reveals a novel link between Notch and BMP pathways potentially involved in the pathogenesis of glaucoma," says Zhou, noting one more tantalizing implication of the paper. "In addition, mutations in Jagged-1 and Notch2 are thought to underlie the human genetic disease known as Alagille Syndrome. Our work may lead to a better understanding of both."
Alagille Syndrome is an inherited childhood disorder causing defects in organ systems including liver, heart and the skeleton. Xie is equally intrigued by potential connections between his group's observations in the mouse eye and Alagille outcomes in humans. Nonetheless, he remains focused on nailing down how perturbation of the Jagged1-Notch2-BMP axis might cause eye disease.
"We now know how to build better mouse mutants to study CB development. In this work we show that Notch regulates BMP signaling but have not yet determined whether alterations in CB structure actually change interocular pressure," he says. "Answering that question is our future goal."
###
Other members of the Stowers team were Shuyi Chen, Ph.D., Michael Duncan, M.D., Karin Gaudenz, Ph.D., Christopher Seidel, Ph.D., Hua Li, Ph.D., Brandy Lewis, and Andrea Moran. Also contributing were Zhipeng Yan, Ph.D., Richard T. Libby, Ph.D., and Amy E. Kiernan, Ph.D, of the University of Rochester Medical Center.
The study was funded in part by the Stowers Institute for Medical Research, the March of Dimes, and a Research to Prevent Blindness Career Development Award.
About the Stowers Institute for Medical Research
The Stowers Institute for Medical Research is a non-profit, basic biomedical research organization dedicated to improving human health by studying the fundamental processes of life. Jim Stowers, founder of American Century Investments, and his wife, Virginia, opened the Institute in 2000. Since then, the Institute has spent over 900 million dollars in pursuit of its mission.
Currently, the Institute is home to nearly 550 researchers and support personnel; over 20 independent research programs; and more than a dozen technology-development and core facilities.
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