
Remarks about the Arithmetic of Graphs
The arithmetic of N, Z, Q, R can be extended to a graph arithmetic where...
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Graph complements of circular graphs
Graph complements G(n) of cyclic graphs are circulant, vertextransitive...
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Complexes, Graphs, Homotopy, Products and Shannon Capacity
A finite abstract simplicial complex G defines the Barycentric refinemen...
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Green functions of Energized complexes
If h is a ringvalued function on a simplicial complex G we can define t...
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Constant index expectation curvature for graphs or Riemannian manifolds
An integral geometric curvature is defined as the index expectation K(x)...
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More on PoincareHopf and GaussBonnet
We illustrate connections between differential geometry on finite simple...
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Poincare Hopf for vector fields on graphs
We generalize the PoincareHopf theorem sum_v i(v) = X(G) to vector fiel...
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A simple sphere theorem for graphs
A finite simple graph G is declared to have positive curvature if every ...
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Energized simplicial complexes
For a simplicial complex with n sets, let W^(x) be the set of sets in G...
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The energy of a simplicial complex
A finite abstract simplicial complex G defines a matrix L, where L(x,y)=...
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A parametrized PoincareHopf Theorem and Clique Cardinalities of graphs
Given a locally injective real function g on the vertex set V of a finit...
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More on Numbers and Graphs
In this note we revisit a "ring of graphs" Q in which the set of finite ...
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DehnSommerville from GaussBonnet
We give a zero curvature proof of DehnSommerville for finite simple gra...
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The average simplex cardinality of a finite abstract simplicial complex
We study the average simplex cardinality Dim^+(G) = sum_x x/(G+1) of...
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A Reeb sphere theorem in graph theory
We prove a Reeb sphere theorem for finite simple graphs. The result brid...
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Cartan's Magic Formula for Simplicial Complexes
Cartan's magic formula L_X = i_X d + d i_X = (d+i_X)^2=D_X^2 relates the...
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Eulerian edge refinements, geodesics, billiards and sphere coloring
A finite simple graph is called a 2graph if all of its unit spheres S(x...
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Combinatorial manifolds are Hamiltonian
Extending a theorem of Whitney of 1931 we prove that all connected dgra...
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The Cohomology for Wu Characteristics
While Euler characteristic X(G)=sum_x w(x) super counts simplices, Wu ch...
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The hydrogen identity for Laplacians
For any finite simple graph G, the hydrogen identity H=LL^(1) holds, w...
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Listening to the cohomology of graphs
We prove that the spectrum of the Kirchhoff Laplacian H0 of a finite sim...
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An Elementary Dyadic Riemann Hypothesis
The connection zeta function of a finite abstract simplicial complex G i...
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One can hear the Euler characteristic of a simplicial complex
We prove that that the number p of positive eigenvalues of the connectio...
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On AtiyahSinger and AtiyahBott for finite abstract simplicial complexes
A linear or multilinear valuation on a finite abstract simplicial compl...
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The strong ring of simplicial complexes
We define a ring R of geometric objects G generated by finite abstract s...
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On a DehnSommerville functional for simplicial complexes
Assume G is a finite abstract simplicial complex with fvector (v0,v1, ....
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A structure from motion inequality
We state an elementary inequality for the structure from motion problem ...
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Space and camera path reconstruction for omnidirectional vision
In this paper, we address the inverse problem of reconstructing a scene ...
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On Ullman's theorem in computer vision
Both in the plane and in space, we invert the nonlinear Ullman transform...
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Oliver Knill
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Mathematician at Harvard University since 2000, Research Fellowship at University of Texas at Austin from 19972000