CAREER: Stochastic processes and embeddings on networks View Homepage


Ontology type: schema:MonetaryGrant     


Grant Info

YEARS

2014-2017

FUNDING AMOUNT

269770 USD

ABSTRACT

Random processes on networks play a major role in a wide range of areas including mathematical physics, machine learning, and theoretical computer science. One such question we will address involves analysing algorithms for detecting sub-communities within a social network by investigating the graph of friendship relations. The proposal addresses questions from combinatorics and computer science about when random combinatorial and computational problems have solutions, such as when there is a colouring in a random graph. Ideas from statistical physics give predictions for these thresholds which we will mathematically prove. It also studies questions of how long it takes random processes on networks, such as the Glauber dynamics Markov chain, to reach their equilibrium distribution and how this depends on their initial starting position. Such processes are used as algorithms for sampling high dimensional distributions. The proposal focuses on development of mathematical theory with a view to better understanding these problems. Finally the proposal will support the development of new graduate courses in discrete probability and stochastic process on random graphs as well as providing research opportunities for graduate and undergraduate researchers. The main theme of this proposal is the development of new theory and applications across a range of stochastic processes on networks. One aspect involves studying phase transitions of Gibbs measures on random graphs, particularly random constraint satisfaction problems. Here we hope to establish conjectures from statistical physics for a range of models such as the chromatic and independence numbers on random graphs. A second theme is the development of new tools for establishing rough isometries and other geometric notions of closeness between random metric spaces. In particular we will consider whether independent copies of Poisson processes, percolation clusters and SLE curves are rough isometries or quasi-symmetries. Finally the proposal will consider Markov random fields such as the Ising model on lattices. At high temperatures it will consider the question of universality of the cutoff phenomena as well as the effect of different initial conditions on the mixing time. At low temperatures it will pursue a better understanding of Ising interfaces in order to establish rapid mixing results. More... »

URL

http://www.nsf.gov/awardsearch/showAward?AWD_ID=1352013&HistoricalAwards=false

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/2208", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/2201", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/2201", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "type": "DefinedTerm"
      }
    ], 
    "amount": {
      "currency": "USD", 
      "type": "MonetaryAmount", 
      "value": "269770"
    }, 
    "description": "Random processes on networks play a major role in a wide range of areas including mathematical physics, machine learning, and theoretical computer science. One such question we will address involves analysing algorithms for detecting sub-communities within a social network by investigating the graph of friendship relations. The proposal addresses questions from combinatorics and computer science about when random combinatorial and computational problems have solutions, such as when there is a colouring in a random graph. Ideas from statistical physics give predictions for these thresholds which we will mathematically prove. It also studies questions of how long it takes random processes on networks, such as the Glauber dynamics Markov chain, to reach their equilibrium distribution and how this depends on their initial starting position. Such processes are used as algorithms for sampling high dimensional distributions. The proposal focuses on development of mathematical theory with a view to better understanding these problems. Finally the proposal will support the development of new graduate courses in discrete probability and stochastic process on random graphs as well as providing research opportunities for graduate and undergraduate researchers. The main theme of this proposal is the development of new theory and applications across a range of stochastic processes on networks. One aspect involves studying phase transitions of Gibbs measures on random graphs, particularly random constraint satisfaction problems. Here we hope to establish conjectures from statistical physics for a range of models such as the chromatic and independence numbers on random graphs. A second theme is the development of new tools for establishing rough isometries and other geometric notions of closeness between random metric spaces. In particular we will consider whether independent copies of Poisson processes, percolation clusters and SLE curves are rough isometries or quasi-symmetries. Finally the proposal will consider Markov random fields such as the Ising model on lattices. At high temperatures it will consider the question of universality of the cutoff phenomena as well as the effect of different initial conditions on the mixing time. At low temperatures it will pursue a better understanding of Ising interfaces in order to establish rapid mixing results.", 
    "endDate": "2017-09-30T00:00:00Z", 
    "funder": {
      "id": "https://www.grid.ac/institutes/grid.457875.c", 
      "type": "Organization"
    }, 
    "id": "sg:grant.3494592", 
    "identifier": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "3494592"
        ]
      }, 
      {
        "name": "nsf_id", 
        "type": "PropertyValue", 
        "value": [
          "1352013"
        ]
      }
    ], 
    "inLanguage": [
      "en"
    ], 
    "keywords": [
      "social networks", 
      "second theme", 
      "other geometric notions", 
      "career", 
      "Poisson process", 
      "major role", 
      "low temperature", 
      "random metric spaces", 
      "research opportunities", 
      "order", 
      "problem", 
      "high temperature", 
      "threshold", 
      "theoretical computer science", 
      "such processes", 
      "embedding", 
      "new theory", 
      "network", 
      "Ising model", 
      "question", 
      "random graphs", 
      "prediction", 
      "wide range", 
      "Gibbs measures", 
      "conjecture", 
      "proposal", 
      "Glauber dynamics Markov chain", 
      "undergraduate researchers", 
      "discrete probability", 
      "random constraint satisfaction problems", 
      "coloring", 
      "computer science", 
      "random process", 
      "cutoff phenomena", 
      "effect", 
      "area", 
      "new graduate course", 
      "statistical physics", 
      "percolation clusters", 
      "phase transition", 
      "stochastic processes", 
      "closeness", 
      "combinatorics", 
      "development", 
      "Ising interface", 
      "SLE curves", 
      "algorithms", 
      "position", 
      "machine learning", 
      "range", 
      "lattice", 
      "computational problems", 
      "mathematical theory", 
      "Markov random field", 
      "high dimensional distributions", 
      "view", 
      "independence number", 
      "rapid mixing results", 
      "such questions", 
      "time", 
      "universality", 
      "model", 
      "graduates", 
      "equilibrium distribution", 
      "main themes", 
      "better understanding", 
      "friendship relations", 
      "mathematical physics", 
      "different initial conditions", 
      "rough isometries", 
      "new tool", 
      "application", 
      "aspects", 
      "solution", 
      "graph", 
      "independent copies", 
      "idea", 
      "sub-communities"
    ], 
    "name": "CAREER: Stochastic processes and embeddings on networks", 
    "recipient": [
      {
        "id": "https://www.grid.ac/institutes/grid.47840.3f", 
        "type": "Organization"
      }, 
      {
        "affiliation": {
          "id": "https://www.grid.ac/institutes/grid.47840.3f", 
          "name": "University of California-Berkeley", 
          "type": "Organization"
        }, 
        "familyName": "Sly", 
        "givenName": "Allan", 
        "id": "sg:person.015324560743.66", 
        "type": "Person"
      }, 
      {
        "member": "sg:person.015324560743.66", 
        "roleName": "PI", 
        "type": "Role"
      }
    ], 
    "sameAs": [
      "https://app.dimensions.ai/details/grant/grant.3494592"
    ], 
    "sdDataset": "grants", 
    "sdDatePublished": "2021-01-20T03:37", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com.uberresearch.data.processor/core_data/20181219_192338/projects/base/nsf_projects_7.xml.gz", 
    "startDate": "2014-08-01T00:00:00Z", 
    "type": "MonetaryGrant", 
    "url": "http://www.nsf.gov/awardsearch/showAward?AWD_ID=1352013&HistoricalAwards=false"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/grant.3494592'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/grant.3494592'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/grant.3494592'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/grant.3494592'


 

This table displays all metadata directly associated to this object as RDF triples.

125 TRIPLES      19 PREDICATES      101 URIs      92 LITERALS      5 BLANK NODES

Subject Predicate Object
1 sg:grant.3494592 schema:about anzsrc-for:2201
2 anzsrc-for:2208
3 schema:amount Nb9e32a2c8eaf4109815483dc13e5fea7
4 schema:description Random processes on networks play a major role in a wide range of areas including mathematical physics, machine learning, and theoretical computer science. One such question we will address involves analysing algorithms for detecting sub-communities within a social network by investigating the graph of friendship relations. The proposal addresses questions from combinatorics and computer science about when random combinatorial and computational problems have solutions, such as when there is a colouring in a random graph. Ideas from statistical physics give predictions for these thresholds which we will mathematically prove. It also studies questions of how long it takes random processes on networks, such as the Glauber dynamics Markov chain, to reach their equilibrium distribution and how this depends on their initial starting position. Such processes are used as algorithms for sampling high dimensional distributions. The proposal focuses on development of mathematical theory with a view to better understanding these problems. Finally the proposal will support the development of new graduate courses in discrete probability and stochastic process on random graphs as well as providing research opportunities for graduate and undergraduate researchers. The main theme of this proposal is the development of new theory and applications across a range of stochastic processes on networks. One aspect involves studying phase transitions of Gibbs measures on random graphs, particularly random constraint satisfaction problems. Here we hope to establish conjectures from statistical physics for a range of models such as the chromatic and independence numbers on random graphs. A second theme is the development of new tools for establishing rough isometries and other geometric notions of closeness between random metric spaces. In particular we will consider whether independent copies of Poisson processes, percolation clusters and SLE curves are rough isometries or quasi-symmetries. Finally the proposal will consider Markov random fields such as the Ising model on lattices. At high temperatures it will consider the question of universality of the cutoff phenomena as well as the effect of different initial conditions on the mixing time. At low temperatures it will pursue a better understanding of Ising interfaces in order to establish rapid mixing results.
5 schema:endDate 2017-09-30T00:00:00Z
6 schema:funder https://www.grid.ac/institutes/grid.457875.c
7 schema:identifier N2115d51a53984ef6af6e81c35acf9a4e
8 N7025b102202442b286ca1be07b438282
9 schema:inLanguage en
10 schema:keywords Gibbs measures
11 Glauber dynamics Markov chain
12 Ising interface
13 Ising model
14 Markov random field
15 Poisson process
16 SLE curves
17 algorithms
18 application
19 area
20 aspects
21 better understanding
22 career
23 closeness
24 coloring
25 combinatorics
26 computational problems
27 computer science
28 conjecture
29 cutoff phenomena
30 development
31 different initial conditions
32 discrete probability
33 effect
34 embedding
35 equilibrium distribution
36 friendship relations
37 graduates
38 graph
39 high dimensional distributions
40 high temperature
41 idea
42 independence number
43 independent copies
44 lattice
45 low temperature
46 machine learning
47 main themes
48 major role
49 mathematical physics
50 mathematical theory
51 model
52 network
53 new graduate course
54 new theory
55 new tool
56 order
57 other geometric notions
58 percolation clusters
59 phase transition
60 position
61 prediction
62 problem
63 proposal
64 question
65 random constraint satisfaction problems
66 random graphs
67 random metric spaces
68 random process
69 range
70 rapid mixing results
71 research opportunities
72 rough isometries
73 second theme
74 social networks
75 solution
76 statistical physics
77 stochastic processes
78 sub-communities
79 such processes
80 such questions
81 theoretical computer science
82 threshold
83 time
84 undergraduate researchers
85 universality
86 view
87 wide range
88 schema:name CAREER: Stochastic processes and embeddings on networks
89 schema:recipient Ndca22ca75a654352a985c0310c6c6d4a
90 sg:person.015324560743.66
91 https://www.grid.ac/institutes/grid.47840.3f
92 schema:sameAs https://app.dimensions.ai/details/grant/grant.3494592
93 schema:sdDatePublished 2021-01-20T03:37
94 schema:sdLicense https://scigraph.springernature.com/explorer/license/
95 schema:sdPublisher Nd1fc299817ad4420903b136e9597322e
96 schema:startDate 2014-08-01T00:00:00Z
97 schema:url http://www.nsf.gov/awardsearch/showAward?AWD_ID=1352013&HistoricalAwards=false
98 sgo:license sg:explorer/license/
99 sgo:sdDataset grants
100 rdf:type schema:MonetaryGrant
101 N2115d51a53984ef6af6e81c35acf9a4e schema:name nsf_id
102 schema:value 1352013
103 rdf:type schema:PropertyValue
104 N7025b102202442b286ca1be07b438282 schema:name dimensions_id
105 schema:value 3494592
106 rdf:type schema:PropertyValue
107 Nb9e32a2c8eaf4109815483dc13e5fea7 schema:currency USD
108 schema:value 269770
109 rdf:type schema:MonetaryAmount
110 Nd1fc299817ad4420903b136e9597322e schema:name Springer Nature - SN SciGraph project
111 rdf:type schema:Organization
112 Ndca22ca75a654352a985c0310c6c6d4a schema:member sg:person.015324560743.66
113 schema:roleName PI
114 rdf:type schema:Role
115 anzsrc-for:2201 schema:inDefinedTermSet anzsrc-for:
116 rdf:type schema:DefinedTerm
117 anzsrc-for:2208 schema:inDefinedTermSet anzsrc-for:
118 rdf:type schema:DefinedTerm
119 sg:person.015324560743.66 schema:affiliation https://www.grid.ac/institutes/grid.47840.3f
120 schema:familyName Sly
121 schema:givenName Allan
122 rdf:type schema:Person
123 https://www.grid.ac/institutes/grid.457875.c schema:Organization
124 https://www.grid.ac/institutes/grid.47840.3f schema:name University of California-Berkeley
125 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...