Наука о сетях

Определение

Наука о сетях (наука о связанности) - научная дисциплина, которая изучает общие черты природных или искусственных сетей, таких как информационные, биологические и социальные сети. Предметом исследования науки о сетях является сетевое представление физических, биологических и социальных явлений, ведущее к построению моделей позволяющих прогнозировать эти явления.

• Network science is an emerging, highly interdisciplinary research area that aims to develop theoretical and practical approaches and techniques to increase our understanding of natural and man made networks.
  • Börner, S. Sanyal, and A. Vespignani, “Network science,” Annual review of information science and technology, vol. 41, no. 1, pp. 537–607, 2007.
  • Today, the computational ability to sample and the scientific need to understand large-scale networks call for a truly interdisciplinary approach to network science. Measurement, modeling, or visualization algorithms developed in one area of research, say physics, might well increase our understanding of biological or social networks. Datasets collected in biology, social science, information science and other fields are used by physicists to identify universal laws.
• A working definition of network science is the study of network representations of physical, biological, and social phenomena leading to predictive models of these phenomena. Initiation of a field of network science would be appropriate to provide a body of rigorous results that would improve the predictability of the engineering design of complex networks and also speed up basic research in a variety of applications areas.
  • National Research Council Network Science / National Research Council, 2005. 124 c.
• Network science is an academic field which studies complex networks such as telecommunication networks, computer networks, biological networks, cognitive and semantic networks, and social networks, considering distinct elements or actors represented by nodes (or vertices) and the connections between the elements or actors as links (or edges).
  • https://en.wikipedia.org/wiki/Network_science
• Наука о сетях занимается выявлением и пониманием строгих математических принципов и законов, которые управляют многообразием сетевых структур, включая биологические, социальные и электронные. Сетевые структуры представляют собой междисциплинарное понятие, применимое к разнообразным системам – от звёздных скоплений и кристаллов до ансамблей элементарных частиц и технических устройств. Сетевые структуры в широком смысле могут состоять из одинаковых или разных узлов. Связи между узлами (ребра) могут быть идентичными или различаться по своей значимости или по иным критериям, быть направленными (как дорога с односторонним движением) или нет.

Наука о сетях Network science - https://en.wikipedia.org/wiki/Network_science - как отдельное направление сформировалось в 21 веке, несмотря на то, что исследование различных сетей в науке, технологии и обществе имеет длительную историю. Взрыв интереса к науке о сетях в первого десятилетия 21-го века коренится в открытии общих закономерностей и принципов, которые лежат в основании структуры и эволюции сложных систем (Сложная система) вне зависимости от их происхождения.

Нетрудно перечислить различия между различными сетями с которыми мы сталкиваемся в природе или обществе:

• узлами метаболической сети являются крошечные молекулы, а ребрами служат цепи химических реакций, подчиняющиеся законам химии и квантовой механики;
• узлами WWW являются веб-документы, а ребрами служат URL ссылки, основанные на компьютерных алгоритмах;
• узлами социальной сети являются люди, а ребрами служат семейные, профессиональные и дружеские и связи.

Существенно отличаются и процессы, которые порождают формирование различных сетей: сети метаболизма сформировались в результате эволюции, продолжавшейся миллиарды лет; Всемирная Паутина строится благодаря коллективным действий миллионов людей и их организаций; социальные сети формируются под воздействием социальных норм, чьи корни уходят в глубь тысячелетий. И не смотря на такое различие в размерах, масштабах, истории и эволюции, сети, лежащие в основании этих сложных систем очень похожи. Архитектура природных, научных и технологических сетей подчиняется общим организационным принципам и для изучения этих систем можно использовать общий набор математических инструментов.

Сетевая наука и карты

• H. Sayama, Introduction to the Modeling and Analysis of Complex Systems. SUNY Geneseo, 2015.
  • Complex systems can be informally defined as networks of many interacting components that may arise and evolve through self-organization. Many realworld systems can be modeled and understood as complex systems, such as political organizations, human cultures/languages, national and international economies, stock markets, the Internet, social networks, the global climate, food webs, brains, physiological systems, and even gene regulatory networks within a single cell; essentially, they are everywhere.
  • Complex systems are networks made of a number of components that interact with each other, typically in a nonlinear fashion. Complex systems may arise and evolve through self-organization, such that they are neither completely regular nor completely random, permitting the development of emergent behavior at macroscopic scales.

Сложные системы - всегда сети. Но, сети не всегда сложные системы. За сложной системой всегда кроется сеть.

Барабаши: - http://barabasi.com/networksciencebook/

To describe the detailed behavior of a system consisting of hundreds to billions of interacting components, we need a map of the system’s wiring diagram. In the past, we lacked the tools to map these networks. It was equally difficult to keep track of the huge amount of data behind them. The Internet revolution, offering effective and fast data sharing methods and cheap digital storage, fundamentally changed our ability to collect, assemble, share, and analyze data pertaining to real networks. Thanks to these technological advances, at the turn of the millenium we witnessed an explosion of map making

• Чтобы описать детальное поведение системы, состоящей из нескольких сотен до нескольких миллиардов взаимодействующих компонентов, необходима карта схема соединений системы. В системе социальной сети карта представляет точный список ваших друзей, затем друзей этих друзей, и так далее. В WWW эта карта представляет перечень веб-страниц, которые ссылаются друг на друга. В живой клетке карта представляет подробный перечень всех взаимодействий и химических реакций с участием генов, белков и метаболитов. Невозможно понять функционирование клетки, если не придавать значения сложным сетевым структурам, посредством которых клеточные белки и промежуточные продукты обмена веществ взаимодействуют друг с другом внутри клетки. Невозможно понять экономическую систему и предсказать экономические банкротства, ели не будет нарисована сеть долговых обязательств, которые характеризуют экономическую систему.

В двадцатом веке не существовало инструментов для сопоставления сетей и отслеживания огромного количества данных, которые стоящих за этими сетями. Интернет-революция, предложившая эффективные и быстрые методы для цифрового хранения и совместного использования данных, коренным образом изменила нашу способность собирать, объединять и анализировать данные, относящиеся к реальным сетям. И когда мы получили возможность видеть и сравнивать все эти различные сети, то оказалось, что за феноменом сложности и за поведением сложных систем скрывается сетевая структура.

Большие данные - Big science of science studies utilize “big data”, i.e., large, complex, diverse, longitudinal, and/or distributed datasets that might be owned by different stakeholders.

Recent work in scientometrics aims to create a map of science encompassing our collective scholarly knowledge. Maps of science can be used to see disciplinary boundaries; the origin of ideas, expertise, techniques, or tools; the birth, evolution, merging, splitting, and death of scientific disciplines; the spreading of ideas and technology; emerging research frontiers and bursts of activity; etc.

• Börner K. [и др.]. Teaching children the structure of science International Society for Optics and Photonics, 2009. 724307–724307 с.

Что такое сетевая наука?

Brandes U. [и др.]. What is network science? // Network Science. 2013. № 1 (1). C. 1–15.

В 2013 году начал выходить журнал Network Science и в первом номере авторы озаботились доказательством того, что такая сетевая наука на самом деле есть и у нее свой объект и свои методы исследования. http://www.journals.cambridge.org/abstract_S2050124213000027 Интересно, что в этой же статье они явно увязали сетевую науку и образование. Рассуждают они о разном, а в качестве прикладного примера приводят учебный класс - думать про класс как про сеть, означает думать совершенно определенным образом, это не про 25 отдельных учеников и даже не 300 возможных диад.

By postulating a friendship network in (say) a school classroom of 25 students, we have taken a theoretical step that is non-trivial. We have supposed that separate individuals are not an adequate representation, moreover that even separate dyads are insufficient; rather, that there is a unity within the classroom that makes it proper to talk of “a” network, not 25 children or 300 dyads. To conceptualize the classroom in network terms is an implicit (and strong) claim that connectedness across individual elements is fundamentally important so that the classroom can be thought of as one “system.” If we accept that ontology, scientific inference is available at multiple levels: the students, the dyads, and indeed the network as a whole. Moreover, the inferences at one level cannot be simply combined (e.g., averaged) to derive inferences at other levels; the networked system is more than a simple aggregation of its constituent elements — it is patterned, not summed.

Начиная рассматривать школьный класс из 25 учеников как сеть друзей мы делаем нетривиальный теоретический шаг. Такое рассмотрение означает признание, что рассмотрение класса как множества отдельных индивидов не позволяют адекватно представить и рассмотреть существующую ситуацию. Даже использование отдельных диад для этого недостаточно, поскольку существует некая общность, объединение в классе, о котором нужно говорить именно как о сети, а не как об отдельных 25 детях или о 300 диадах. Осмысление класса в сетевых терминах предполагает неявное (и сильное) утверждение принципиальной важности связей между элементами, которые позволяют рассматривать класс как систему. За принятием сетевой онтологии последуют изменения на всех уровнях научного рассмотрения - и отдельных учеников, и диад и всей сети. Кроме того, выводы на одном уровне не могут быть просто объединены (например, усреднены) для получения выводов на других уровнях; сетевая система больше, чем просто агрегация составляющих его элементов.

Network science & STEM

Как пересекаются STEM и Сетевая наука

Осознание важности сетевой науки привело к тому, что в США и Западной Европе были созданы центры сетевых исследований, а на базе этих центров были организованы учебные курсы для студентов и школьников. При этом сетевая наука рассматривалась и как область знаний, необходимая жителю 21 века и как средство привлечения молодёжи к STEM.

Центры сетевой науки:

• https://cns.ceu.edu/ Центр Сетевой Науки в Центральном Европейском Университете - Венгрия, Будапешт, Барабаши
  • https://en.wikipedia.org/wiki/CEU_Center_for_Network_Science
  • И у них свое определение https://cns.ceu.edu/node/25884 Network science, as a maturing field, offers a unique perspective to tackle complex problems, impenetrable to linear-proportional thinking. Rather than focusing solely on the internal properties of the parts that make up social systems, the network perspective draws attention to the relations between the parts. Network analysis thus complements the classical atomistic Hobbesian social-scientific approach with a perspective that is more in line with how August Comte defined social science, i.e. the study of human relations. The concept of networks has come to pervade modern society. In our everyday experience we routinely use online social network services, we hear reports on the operation of terrorist networks, we notice the cascading disturbances in global finance networks, and we speculate on the six degrees of separation to celebrities and presidents. The science of networks is emerging as a scientific discipline that examines exactly these kinds of interconnections, and many more. Although networks and networking indeed have turned into modern everyday buzzwords, the network-scientific approach - with its formal set of analytical tools - is indeed applicable in the study of almost any spatiotemporal social system and phenomena.

Наука о сетях и сетевые сообщества

Сетевое сообщество ранее определялось как множество людей, общающихся между собой при помощи сетевых сервисов. С точки зрения науки о сетях - это слабое определение, потому что оно не позволяет что-либо измерить. Насколько одно сообщество сообщнее другого сообщества?

In network science we call a community a group of nodes that have a higher likelihood of connecting to each other than to nodes from other communities.

В науке о сетях сообщество - это группа узлов, связанных между собою большим числом связей, чем с узлами из других сообществ. Сообщества - это локально плотно связные подграфы в сети. In other words, all members of a community must be reached through other members of the same community (connectedness)

A network’s community structure is uniquely encoded in its wiring diagram.

Сильные сообщества

C is a strong community if each node within C has more links within the community than with the rest of the graph

С является сильным сообществом, если каждый узел в пределах C имеет больше связей внутри сообщества, чем с остальной частью графа

Слабое сообщество

C is a weak community if the total internal degree of a subgraph exceeds its total external degree

The higher is M for a partition, the better is the corresponding community structure

Учебные курсы:

• http://www.bu.edu/networks/

http://www.bu.edu/networks/

• • NetSci High has been our first leap in this pursuit, immersing high school students and teachers in the burgeoning field of network science, a core pathway to making sense of many kinds of Big Data. Each year, NetSci High begins with an intensive residential summer workshop using a network lens to understand and find solutions to complex social, health and environmental problems. Students and teachers are introduced to network science foundations including graph theory, statistical inferencing, data mining, systems theory, and information visualization.
  • Many real-world systems can be understood as complex systems, where critically important information resides in the relationships between the parts and not necessarily within the parts themselves.
• Network Science: Methods and Applications http://www.cc.gatech.edu/~dovrolis/Courses/NetSci
  • It is often the case that complex systems, both living and man-made, can be represented as static or dynamic networks of many interacting components. These components are typically much simpler in terms of behavior or function than the overall system, implying that the additional complexity of the latter is an emergent network property. Network science is a new discipline that investigates the topology and dynamics of such complex networks, aiming to better understand the behavior, function and properties of the underlying systems. The applications of network science cover physical, informational, biological, cognitive, and social systems. In this course, we will study algorithmic, computational, and statistical methods of network science, as well as applications in communications, biology, ecology, brain science, sociology and economics. The course hopes to attract students from different academic backgrounds and research interests (including math, physics, engineering, biology, neuroscience or sociology).
• https://www.cs.purdue.edu/homes/agebreme/Networks/
  • The course seeks to introduce fundamental elements of the emerging science of complex networks, with emphasis on social and information networks. Students will be introduced to select mathematical and computational methods used to analyze networks, models used to understand and predict behavior of networked systems, and theories used to reason about network dynamics. Students will also be exposed to current research in the field, and they will be given an opportunity to explore a chosen topic through a semester project.

L. Sheetz, V. Dunham, and J. Cooper, “Professional development for network science as a multi-disciplinary curriculum tool,” in 2015 IEEE Integrated STEM Education Conference (ISEC), 2015, pp. 178–182.

• To be successful in the 21st century, students must have a fundamental knowledge of complex networks which allows them to explore the interconnectedness of our world. Network science, a relatively new field of study, represents a fundamental shift away from reductionism to a more complex real world approach to problem solving which looks at interactions between components as well as the components themselves in a system. It is a tool that assists researchers and students to make connections needed to solve complex challenges and integrate abstract ideas.

• Network Science for the Next Generation - Collaborative Research
  • The Network Science project is a three year ITEST strategies project designed to engage 120 disadvantaged high school students (grades 10-11) and up to 30 high school STEM teachers from Boston and New York urban schools in a network science research based program, using cutting edge computer modeling research technology. Working with graduate student mentors, Network Science students and teachers will: (a) learn about the emerging discipline of network science, (b) construct and analyze science networks using computations and data visualizations, (c) use networks to solve problems across STEM domains (e.g., energy, communications, and diseases) through collaborative research projects and integrated technology, and (d) present their research at an annual Network Science research conference.

Network Science - как чудесное средство для вовлечения в STEM

Networks are pervasive across all aspects of life: biological, physical, economic, and social and our society continues to become ever more connected through the use of social media tools that allow for instantaneous and targeted communication and better situation awareness. This inherently interdisciplinary and cross-generational nature makes network science the perfect tool to engage students in STEM fields. Components of networks have been used as a tool for teaching math and computer science for many years. Scientists have expanded these efforts by developing and sharing informal outreach materials to demonstrate how network science can successfully be used to engage students in STEM fields.

Положения от K. Börner, “STEM: Individual, Local, and Global Flows and Activity Patterns,” ResearchGate, Jan. 2009.

1. Science/Economy/STEM is Global and needs to be understood globally (but optimized locally).
2. STEM is Evolving Dynamically and has to be studied using dynamically evolving (not static) datasets and complex systems approaches.
3. Open Data (also teaching materials) and Open Code empowers many to help increase our understanding of what works and why.

Кати Бёрнер -

• Additionally, the project will collect, integrate and analyze data on network education and its impact on decision making (DM). This data will be used to develop a quantitative model of a dynamic DM network. Developing a cognitive/educational impact model for network based decision making would be substantial contribution in decision sciences.

• Harrington H.A. et al. Commentary: Teach network science to teenagers // Network Science. 2013. Vol. 1, № 2. P. 226–247.
• Sheetz L., Dunham V., Cooper J. Professional development for network science as a multi-disciplinary curriculum tool // 2015 IEEE Integrated STEM Education Conference (ISEC). 2015. P. 178–182.
  • To be successful in the 21st century, students must have a fundamental knowledge of complex networks which allows them to explore the interconnectedness of our world. Network science, a relatively new field of study, represents a fundamental shift away from reductionism to a more complex real world approach to problem solving which looks at interactions between components as well as the components themselves in a system. It is a tool that assists researchers and students to make connections needed to solve complex challenges and integrate abstract ideas. While this field has primarily engaged students at a graduate level, recently a growing number of new undergraduate courses have been offered and for a small number of high school students there have been opportunities to participate in research. However, initiatives have reached a relatively small number of students. In an effort to bring network thinking to more students, a professional development course was developed to introduce more teachers to network science and show how it can be utilized as a multi-disciplinary tool within their current curriculum.
• Cramer C. et al. NetSci High: Bringing Network Science Research to High Schools // Complex Networks VI / ed. Mangioni G. et al. Springer International Publishing, 2015. P. 209–218.
  • https://prezi.com/5dnwze2bc8n7/network-science-as-a-stem-tool/
  • We present NetSci High, our NSF-funded educational outreach program that connects high school students who are underrepresented in STEM (Science Technology Engineering and Mathematics), and their teachers, with regional university research labs and provides them with the opportunity to work with researchers and graduate students on team-based, year-long network science research projects, culminating in a formal presentation at a network science conference. This short paper reports the content and materials that we have developed to date, including lesson plans and tools for introducing high school students and teachers to network science; empirical evaluation data on the effect of participation on students’ motivation and interest in pursuing STEM careers; the application of professional development materials for teachers that are intended to encourage them to use network science concepts in their lesson plans and curriculum; promoting district-level interest and engagement; best practices gained from our experiences; and the future goals for this project and its subsequent outgrowth.

Сетевая грамотность

Сетевая наука и обучение https://sites.google.com/a/binghamton.edu/netscied/ - Network science in Education

Network literacy - сетевая грамотность

As our world becomes increasingly connected through the use of networks that allow instantaneous communication and the spread of information, the degree of people’s understanding of how these networks work will play a major role in determining how much society will benefit from this heightened connectivity. In short, a networked society requires network literacy: basic knowledge about how networks can be used as a tool for discovery and decision-making, and about both their potential benefits and pitfalls, made accessible for all people living in today’s networked world. Moreover, because even young children interact with networks all day, every day, it is important that network literacy begins at a young age, and because networks are present in all aspects of contemporary life, the consideration of networks should be reflected throughout teaching practice in a cross-disciplinary manner. Yet despite the importance and ubiquity of networks, the study of networks is absent from current educational systems.

• Sayama H. et al. What are essential concepts about networks? // jcomplexnetw. 2016. Vol. 4, № 3. P. 457–474.
  • Какие понятия в области науки о сетях являются наиболее существенными?

Сравнение сетей различного типа

• N - число узлов
• L - число связей
• К - average degree - среднее число связей у узла

Network	Nodes	Links	Directed / Undirected	N	L	‹K›
Internet	Routers	Internet connections	Undirected	192,244	609,066	6.34
WWW	Webpages	Links	Directed	325,729	1,497,134	4.60
Power Grid	Power plants, transformers	Cables	Undirected	4,941	6,594	2.67
Mobile-Phone Calls	Subscribers	Calls	Directed	36,595	91,826	2.51
Email	Email addresses	Emails	Directed	57,194	103,731	1.81
Science Collaboration	Scientists	Co-authorships	Undirected	23,133	93,437	8.08
Actor Network	Actors	Co-acting	Undirected	702,388	29,397,908	83.71
Citation Network	Papers	Citations	Directed	449,673	4,689,479	10.43
E. Coli Metabolism	Metabolites	Chemical reactions	Directed	1,039	5,802	5.58
Protein Interactions	Proteins	Binding interactions	Undirected	2,018	2,930	2.90

см. http://barabasi.com/networksciencebook/chapter/1

Ссылки

1. Scholtes I. Understanding complex systems: When Big Data meets network science // it - Information Technology. 2015. № 4 (57). C. 252–256.
   • http://www.ingoscholtes.net/research/publications
2. http://networkscience.igert.ucsb.edu/
3. Krieger D.J., Belliger A. Interpreting Networks: Hermeneutics, Actor-Network Theory & New Media / D.J. Krieger, A. Belliger, transcript Verlag, 2014. 205 c.
4. http://www.network-science.org/
   • http://www.books.network-science.org/ книги по сетевой науке
5. http://netwiki.amath.unc.edu/ - вики о сетевой науке
6. http://www.empatika.com/blog/santa-fe-newman-emerging-network-science Лекция Марка Ньюмана (SFI) – Зарождающаяся наука о сетях
7. Уоттс Д. Здравый смысл врет. Почему не надо слушать свой внутренний голос. Litres, 2015. 458 p.
   • http://www.e-reading.club/bookreader.php/1017340/Uotts_-_Zdravyy_smysl_vret..html текст книги Уоттса

Нейробиология - Мозг как сеть

• Rubinov M., Sporns O. Complex network measures of brain connectivity: Uses and interpretations // NeuroImage. 2010. № 3 (52). C. 1059–1069.
  • https://sites.google.com/site/bctnet/
• The Brain as a Complex System: Using Network Science as a Tool for Understanding the Brain https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3621511/ - как одно из направлений нейробиологии
  • This model is appealing to the study of brain connectivity, as the brain can be viewed as a system with various interacting regions that produce complex behaviors. In practice, graph metrics such as clustering coefficient, path length, and efficiency measures are often used to characterize system properties. Centrality metrics such as degree, betweenness, closeness, and eigenvector centrality determine critical areas within the network. Community structure is also essential for understanding network organization and topology.

Данные для изучения

Network data sets

• http://www-personal.umich.edu/~mejn/netdata/ Открытая коллекция данных для сетевых исследований (2013 - последние добавления)
• http://www3.nd.edu/~networks/resources.htm Коллекция Барабаши с указанием публикаций
• http://snap.stanford.edu/data/ Stanford Large Network Dataset Collection - в основном данные по интернет сетям
• http://vlado.fmf.uni-lj.si/pub/networks/data/default.htm Payek коллекции
• https://networkdata.ics.uci.edu/ The UCI Network Data Repository is an effort to facilitate the scientific study of networks.

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