An essential part of an expert-finding task, such as matching reviewers to submitted papers, is the ability to model the expertise of a person based on documents. We evaluate several measures of the association between an author in an existing collection of research papers and a previously unseen document. We compare two language model based approaches with a novel topic model, Author-Persona-Topic (APT). In this model, each author can write under one or more "personas," which are represented as independent distributions over hidden topics. Examples of previous papers written by prospective reviewers are gathered from the Rexa database, which extracts and disambiguates author mentions from documents gathered from the web. We evaluate the models using a reviewer matching task based on human relevance judgments determining how well the expertise of proposed reviewers matches a submission. We find that the APT topic model outperforms the other models.

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Expertise modeling for matching papers with reviewers

A signed graph is a graph whose edges are labeled by signs. This is a bibliography of signed graphs and related mathematics. Several kinds of labelled graph have been called "signed" yet are mathematically very different. I distinguish four types: Group-signed graphs: the edge labels are elements of a 2-element group and are multiplied around a polygon (or along any walk). Among the natural generalizations are larger groups and vertex signs. Sign-colored graphs, in which the edges are labelled from a two-element set that is acted upon by the sign group: - interchanges labels, + leaves them unchanged. This is the kind of "signed graph" found in knot theory. The natural generalization is to more colors and more general groups —  or no group. Weighted graphs, in which the edge labels are the elements +1 and -1 of the integers or another additive domain. Weights behave like numbers, not signs; thus I regard work on weighted graphs as outside the scope of the bibliography — ex cept (to some extent) when the author calls the weights "signs". Labelled graphs where the labels have no structure or properties but are called "signs" for any or no reason.

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A Mathematical Bibliography of Signed and Gain Graphs and Allied Areas

Typical brain networks consist of many peripheral regions and a few highly central ones, i.e., hubs, playing key functional roles in cerebral inter-regional interactions. Studies have shown that networks, obtained from the analysis of specific frequency components of brain activity, present peculiar architectures with unique profiles of region centrality. However, the identification of hubs in networks built from different frequency bands simultaneously is still a challenging problem, remaining largely unexplored. Here we identify each frequency component with one layer of a multiplex network and face this challenge by exploiting the recent advances in the analysis of multiplex topologies. First, we show that each frequency band carries unique topological information, fundamental to accurately model brain functional networks. We then demonstrate that hubs in the multiplex network, in general different from those ones obtained after discarding or aggregating the measured signals as usual, provide a more accurate map of brain's most important functional regions, allowing to distinguish between healthy and schizophrenic populations better than conventional network approaches.

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Mapping Multiplex Hubs in Human Functional Brain Networks.

The permanent-determinant method and its generalization, the Hafnian-Pfaffian method, are methods to enumerate perfect matchings of plane graphs that was discovered by P. W. Kasteleyn. We present several new techniques and arguments related to the permanent-determinant with consequences in enumerative combinatorics. Here are some of the results that follow from these techniques: 
1. If a bipartite graph on the sphere with 4n vertices is invariant under the antipodal map, the number of matchings is the square of the number of matchings of the quotient graph. 
2. The number of matchings of the edge graph of a graph with vertices of degree at most 3 is a power of 2. 
3. The three Carlitz matrices whose determinants count a x b x c plane partitions all have the same cokernel. 
4. Two symmetry classes of plane partitions can be enumerated with almost no calculation.

An exploration of the permanent-determinant method

The existing results on the leader-following attitude consensus for multiple rigid spacecraft systems assume that all the parameters of the spacecraft systems are known exactly and the information flow among the followers is bidirectional. In this paper, we remove these two assumptions. First, by introducing a new Lyapunov function, we allow the communication network to be directed. Second, we convert the leader-following consensus problem into an adaptive stabilization problem of a well defined error system. Then, under the standard assumption that the state of the leader system can reach every follower through a directed path, we further show that this stabilization problem is solvable by a distributed adaptive control law. Moreover, we also present the sufficient condition for guaranteeing the convergence of the estimated parameters to the unknown actual parameters.

Leader-following adaptive consensus of multiple uncertain rigid spacecraft systems

The Laplacian is another important matrix associated with a graph, and the Laplacian spectrum is the spectrum of this matrix. We will consider the relationship between structural properties of a graph and the Laplacian spectrum, in a similar fashion to the spectral graph theory of previous chapters. We will meet Kirchhoff’s expression for the number of spanning trees of a graph as the determinant of the matrix we get by deleting a row and column from the Laplacian. This is one of the oldest results in algebraic graph theory. We will also see how the Laplacian can be used in a number of ways to provide interesting geometric representations of a graph. This is related to work on the Colin de Verdiere number of a graph, which is one of the most important recent developments in graph theory.

The Laplacian of a Graph

Let X be a graph with an orientation σ and let D be the incidence matrix of X σ. In this chapter we continue the study of how graph-theoretic properties of X are reflected in the algebraic properties of D. As previously, the orientation is merely a device used to prove the results, and the results themselves are independent of which particular orientation is chosen. Let ℝ E and ℝ v denote the real vector spaces with coordinates indexed by the edges and vertices of X, respectively. Then the column space of D T is a subspace of ℝ E , called the cut space of X. The orthogonal complement of this vector space is called the flow space of X.

Cuts and Flows

This chapter provides an introduction to some of the graph theory associated with knots and links. The connection arises from the description of the shadow of a link diagram as a 4-valent plane graph. The link diagram is determined by a particular eulerian tour in this graph, and consequently many operations on link diagrams translate to operations on eulerian tours in plane graphs. The study of eulerian tours in 4-valent plane graphs leads naturally to the study of a number of interesting combinatorial objects, such as double occurrence words, chord diagrams, circle graphs, and maps. Questions that are motivated by the theory of knots and links can often be clarified or solved by being reformulated as a question in one of these different contexts.

Knots and Eulerian Cycles

An arc in a graph is an ordered pair of adjacent vertices, and so a graph is arc-transitive if its automorphism group acts transitively on the set of arcs. As we have seen, this is a stronger property than being either vertex transitive or edge transitive, and so we can say even more about arc-transitive graphs. The first few sections of this chapter consider the basic theory leading up to Tutte’s remarkable results on cubic arc-transitive graphs. We then consider some examples of arc-transitive graphs, including three of the most famous graphs of all: the Petersen graph, the Coxeter graph, and Tutte’s 8-cage.

Arc-Transitive Graphs

If X is a graph with incidence matrix B, then the adjacency matrix of its line graph L(X) is equal to B T B-2I. Because B T B is positive semidefinite, it follows that the minimum eigenvalue of L(X) is at least −2. This chapter is devoted to showing how close this property comes to characterizing line graphs. The main result is a beautiful characterization of all graphs with minimum eigenvalue at least −2. One surprise is that the proof uses several seemingly unrelated combinatorial objects. These include generalized quadrangles with lines of size three and root systems, which arise in connection with a number of important problems, including the classification of Lie algebras.

Gordon Royle

Papers

The Laplacian of a Graph

Cuts and Flows

Knots and Eulerian Cycles

Arc-Transitive Graphs

Line Graphs and Eigenvalues