src/pdf/blasten_publications.tex

@@ -36,6 +36,11 @@
 \subsection*{Submitted}
 
 \begin{itemize}
+\item \textsc{E. Bl{\r a}sten}, \textsc{H. Isozaki},
+  \textsc{M. Lassas}, \textsc{J. Lu}: \textit{The Gel'fand's inverse
+    problem for the graph Laplacian},
+  \href{https://arxiv.org/abs/2101.10026}{arXiv:2101.10026}.
+
 \item \textsc{E. Bl{\r a}sten}, \textsc{H. Liu}, \textsc{J. Xiao}:
   \textit{On an electromagnetic problem in a corner and its
     applications},

src/research.html

@@ -122,6 +122,18 @@
             <h3>Submitted</h3>
             <ol reversed>
               <li>
+		<a class="anchor" id="Blasten-Isozaki-Lassas-Lu_2021"></a>
+                <span class="ref-authors">E. Blåsten, H. Isozaki,
+                  M. Lassas, J. Lu,</span>
+                <span class="ref-title">The Gel'fand's inverse problem
+                  for the graph Laplacian.</span>
+                <div class="ref-links">
+                  <a href="#desc_Blasten-Isozaki-Lassas-Lu_2021">Description</a>
+                  <a href="https://arxiv.org/abs/2101.10026">Preprint</a>
+		</div>
+	      </li>
+
+              <li>
 		<a class="anchor" id="Blasten-Liu-Xiao-2019"></a>
                 <span class="ref-authors">E. Blåsten, H. Liu, J. Xiao,</span>
                 <span class="ref-title">On an electromagnetic problem
@@ -581,6 +593,51 @@
 	  <dl>
             <dt>
 	      <a class="anchor"
+	      id="desc_Blasten-Isozaki-Lassas-Lu_2021"></a>
+              <a href="#Blasten-Isozaki-Lassas-Lu_2021">
+                <span class="ref-authors">E. Blåsten, H. Isozaki,
+                  M. Lassas, J. Lu,</span>
+                <span class="ref-title">The Gel'fand's inverse problem
+                  for the graph Laplacian.</span>
+              </a>
+            </dt>
+            <dd>
+	      <p>
+		We consider the graph Laplacian, a discrete operator
+		defined on simple graphs, and its spectrum and
+		eigenfunctions on a weighted simple graph. We prove
+		that knowing the spectrum and Neumann boundary data of
+		the associated Neumann eigenfunctions determines the
+		structure of the graph and also the unknown weights
+		and potential function for a class of graph that
+		satisfy a so-called "two-points condition."
+	      </p>
+	      <p>
+		The above assumes that the graph has
+		a <em>boundary</em>. This is simply a subset of the
+		graph's vertices. For our result, it cannot be an
+		arbitrary subset, but must be "large enough". It must
+		at least be a <em>resolving set</em> for the
+		graph. This means that no two different points in the
+		graph have the exact same distances to every single
+		boundary point.
+	      </p>
+	      <p>
+		The two-point condition means that any subset of
+		interior vertices that has at least two elements must
+		have two <em>extreme points</em>. An extreme point of
+		a set <i>S</i> is a point which is the unique closest
+		point of <i>S</i> to some boundary point.
+	      </p>
+	      <p>
+		Cases which satisfy our assumptions include standard
+		lattices and their perturbations. In particular loops
+		are not a problem for our method.
+	      </p>
+            </dd>
+
+            <dt>
+	      <a class="anchor"
 	      id="desc_Blasten-Paivarinta-Sadique-2020"></a>
               <a href="#Blasten-Paivarinta-Sadique-2020">
                 <span class="ref-authors">E. Blåsten, L. Päivärinta,