<mods:mods xmlns:mods="http://www.loc.gov/mods/v3" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" ID="malvai" xsi:schemaLocation="http://www.loc.gov/mods/v3 http://www.loc.gov/mods/v3/mods-3-6.xsd">
   <mods:titleInfo>
      <mods:title>Generalizations of chip-firing games</mods:title>
   </mods:titleInfo>
   <mods:name type="personal">
      <mods:namePart>Malvai, Harjasleen</mods:namePart>
      <mods:role>
         <mods:roleTerm type="text">creator</mods:roleTerm>
      </mods:role>
   </mods:name>
   <mods:name type="personal">
      <mods:namePart>Klivans, Caroline</mods:namePart>
      <mods:role>
         <mods:roleTerm type="text">advisor</mods:roleTerm>
      </mods:role>
      <mods:affiliation>Brown University. Division of Applied Mathematics</mods:affiliation>
   </mods:name>
   <mods:name xmlns:xlink="http://www.w3.org/1999/xlink" type="corporate" usage="primary" xlink:type="simple">
      <mods:namePart>Brown University. Undergraduate Teaching and Research Award</mods:namePart>
      <mods:role>
         <mods:roleTerm type="text">research program</mods:roleTerm>
      </mods:role>
   </mods:name>
   <mods:typeOfResource>still image</mods:typeOfResource>
   <mods:genre authority="aat" usage="primary">posters</mods:genre>
   <mods:originInfo>
      <mods:place>
         <mods:placeTerm type="text">Providence</mods:placeTerm>
      </mods:place>
      <mods:publisher>Brown University</mods:publisher>
      <mods:dateCreated keyDate="yes" encoding="w3cdtf">2015-08-07</mods:dateCreated>
   </mods:originInfo>
   <mods:physicalDescription>
      <mods:extent supplied="yes">1 poster</mods:extent>
      <mods:digitalOrigin>reformatted digital</mods:digitalOrigin>
   </mods:physicalDescription>
   <mods:language usage="primary">
      <mods:languageTerm>eng</mods:languageTerm>
   </mods:language>
   <mods:abstract>Chip-firing games first occurred independently in physics, economics and
      mathematics. In the graphical case, we consider a graph with integer number of chips placed on
      each vertex, allowing each vertex to fire, or give chips to its neighbors, under certain
      rules. The version that is more often studied is the chip-firing game with a sink vertex,
      normalizing the total number of chips to zero. Even in the graphical case, one can use a
      vector for representing the chip configuration and the graph laplacian for firings. Further
      generalizations include higher dimensional graphs, M-matrices and general invertible matrices.
      In each of these situations, we are concerned with various notions of stability and the
      relationships between them--this is related with a physical notion of energy minimization.
      Given that prior work hasn't been done on general invertible matrices, we worked to examine
      the extensions of the notions to this case and the consequences of these
      definitions.</mods:abstract>
   <mods:subject authority="local">
      <mods:topic>Invertible matrices</mods:topic>
   </mods:subject>
   <mods:subject authority="local">
      <mods:topic>Chip-firing</mods:topic>
   </mods:subject>
<mods:identifier xmlns:xlink="http://www.w3.org/1999/xlink" type="doi">10.26300/ec3c-3j73</mods:identifier></mods:mods>