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Applying mathematics takes 'friendship paradox' beyond averages

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The friendship paradox is the observation that the degrees of the neighbors of a node within any network will, on average, be greater than the degree of the node itself. In other words: your friends probably have more friends than you do.
While the standard framing of the friendship paradox is essentially about averages, significant variations occur too.
In the
Journal of Complex Networks, Santa Fe Institute and University of Michigan researchers George Cantwell, Alec Kirkley, and Mark Newman address this by developing the mathematical theory of the friendship paradox.
Some people have lots of friends, while others have only a few. Unless you have good reason to believe otherwise, it s reasonable to assume you have roughly an average number of friends. ....

United States , Mark Newman , Alec Kirkley , George Cantwell , Journal Of Complex Networks , Santa Fe Institute , University Of Michigan , Complex Networks , Mathematics Statistics , Systems Chaos Pattern Formation Complexity , Social Behavioral Science , ஒன்றுபட்டது மாநிலங்களில் , குறி புதியவர் , ஜார்ஜ் கான்ட்வெல் , சாந்தா ஃபே நிறுவனம் , பல்கலைக்கழகம் ஆஃப் மிச்சிகன் , சிக்கலான நெட்வொர்க்குகள் , கணிதம் புள்ளிவிவரங்கள் ,

Life stage differences shield ecological communities from collapse

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A new study by ecologist André de Roos shows that differences between juveniles and adults of the same species are crucial for the stability of complex ecological communities. The research, published in
Proceedings of the National Academy of Sciences, represents a major advance in ecological modeling at a time when biodiversity is declining and species around the world are rapidly going extinct.
Up to now, ecological models have focused exclusively on the interactions between species, ignoring the variations within them. The dragonflies, frogs, trout, and phytoplankton in a freshwater pond, for example, would be represented as nodes in a network, connected by edges that represent how each species feeds on the others. ....

Robert May , Proceedings Of The National Academy Sciences , National Academy , Ecology Environment , Marine Freshwater Biology , Pollution Remediation , Population Biology , Algorithms Models , Systems Chaos Pattern Formation Complexity , Climate Change , ராபர்ட் இருக்கலாம் , தேசிய கலைக்கழகம் ,

The Mathematical Model of the Mind

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IMAGE: Cover for The Subcritical Brain: A Synergy of Segregated Neural Circuits in Memory, Cognition and Sensorimotor Control.
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Credit: World Scientific
What is perhaps the most wonderous and fascinating creation of nature, the brain, attracting, on one level or another, over centuries, human curiosity, becomes a welcoming territory to be explored from a fresh new perspective of mathematical and cortical synergies in Prof. Yoram Baram s latest publication.
Have over a hundred years of brain research revealed all its secrets? An incredibly large body of knowledge and understanding of brain and mind does not seem to have eliminated the sense of a missing link connecting it all. ....

Technion Roy Mattas , Yoram Baram , Technion Centre For Research , Computer Science Department , Research Award For Best Platform Presentation , James Research Centre , Intelligent Systems , Subcritical Brain , Segregated Neural Circuits , Sensorimotor Control , Computer Science , Aeronautical Engineering , Electrical Engineering , Senior Research Associate , National Research Council , Research Centre , Research Award , Best Platform Presentation , Winnipeg Chair , Technion Centre , Science Math , Systems Chaos Pattern Formation Complexity , Medicine Health , Clinical Trials , Parkinsons Disease , Disabled Persons ,

Trust the machine -- it knows what it is doing

Machine learning, when used in climate science builds an actual understanding of the climate system. This means we can trust machine learning and further its applications in climate science, say the authors. ....

France General , United Kingdom , Michael Ghil , Valerio Lucarini , Manuel Santos Guti , University Of Copenhagen , University Of Reading , Weizmann Institute , Ecole Normale Sup , European Horizon , Empirical Model Reduction , Climate Science , Earth Science , Systems Chaos Pattern Formation Complexity , Computer Science , Robotry Artificial Intelligence , Climate Change , பிரான்ஸ் ஜநரல் , ஒன்றுபட்டது கிஂக்டம் , மைக்கேல் கில் , பல்கலைக்கழகம் ஆஃப் கோபெந்ஹேகந் , பல்கலைக்கழகம் ஆஃப் ரீடிஂக் , வெய்ஸ்மேன் நிறுவனம் , ஐரோப்பிய அடிவானம் , காலநிலை அறிவியல் ,

A new model enables the recreation of the family tree of complex networks

In a new study published in Proceedings of the National Academy of Sciences (PNAS), a research team of the Institute of Complex Systems of the UB (UBICS) analysed the time evolution of real complex networks and developed a model in which the emergence of new nodes can be related to pre-existing nodes, similarly to the evolution of species in biology. ....

Proceedings Of The National Academy Sciences , National Academy , Complex Systems , Mathematics Statistics , Systems Chaos Pattern Formation Complexity , Technology Engineering Computer Science , தேசிய கலைக்கழகம் , சிக்கலான அமைப்புகள் , கணிதம் புள்ளிவிவரங்கள் ,